First off, it's important to note that it's impossible to create a build that encompasses the entire aspect of any champion. In order to get a full picture and a more flexible feel of a champion, I suggest you read several different builds and most off all gain experience through playing. No build can replace that.

This build will try to go rather indepth into a semi-nuke, semi-support Morgana that prefers to play solo top. For this reason, she is also really tough and has a very high survivability. This build will focus on making sure you will hardly ever die, while still doing a lot of damage and support/control. The build also works well as a mid, but isn't particularly well suited as a support in the bot lane.

Do note that I will severely elaborate on several occasions, so simply skip uninteresting parts if TLDR.

You'll also notice I'll use several colors to indicate my personal preference concerning certain concepts about Morgana. The order of good to bad is quite natural.

Morgana isn't a standard pick in most games and she hasn't had a nerf or buff for quite a while. She can be considered to be a solid champion, but often doesn't excell.

I will now give a short description of her most important plusses:

• Her passive Soul Siphon is one of the best in the game. Though it's hard to compare passives, I feel that Morgana's helps me in a very active and noticable way. It's synergy with her other abilities should not be underestimated.
• Her control is quite extensive. Both her Dark Binding as her Soul Shackles can decide the outcome of teamfights. Combined with a Rylai's Crystal Scepter, her Tormented Shadow serves well too.
• She's extremely survivable. This is due to a combination of the items, her spell vamp, her control, etc... though, so don't rely on it too strongly for all builds.
• She can hold a 1vs2 with ease. It's not likely you'll have these kind of situation at high elo, but in normal games it's a common challenge.

But there are some downsides as well:

• Morgana has remarkably high cooldowns and not a single spammable skill. I'm not completely happy about that.
• She's very mana-intensive.

EDIT: The 10/08/2011 patch reduced the cooldowns of her Dark Binding and Soul Shackles. Also the mana-cost of her most farming ability Tormented Shadow was severely lowered. The issues described above are no longer as acute.

I'll keep this one rather short. Everyone picks runes to their own liking and playstyle. I'll simply discuss the runes I choose and some alternatives.

• The Greater Glyph of Cooldown Reduction is an obvious choice because her cooldowns are simply so high. Standard alternatives include Greater Glyph of Scaling Ability Power and Greater Glyph of Ability Power.
• For marks I pick Greater Mark of Magic Penetration for obvious reasons.
• Greater Quintessence of Health is a personal choice for survivablity begingame. It's a solid pick for going solo top, especially when you somehow get a 1vs2.
• For Morgana, seals are a wildcard in my personal experience. I prefer to take flat armor with the Greater Seal of Armor because it takes the edge off of those early jungle ganks on top. At begingame a lot of damage is done by auto-attacking due to high cooldowns and the lower number of abilities, so it's a solid damage reduction. It also helps against the minions when you're harassing.

I primarily focus on the utility department to fix the mana-inefficiency which is rather prominent begingame. It's all pretty standard, as well as the magic penetration in the offence masteries. I also pick the Clarity utility to make it viable.

This'll be a quite lengthy description of the abilities and their uses. I'm not kidding, it'll be way to detailed and obvious for seasoned players and maybe too complex and long for starters, but better to give a decent picture than just a small slice. If you're confident of your abilities, just skip this part altogether.

Soul Siphon

This is Morgana's awesome passive. Its effect is not situational and will always be of great use to you. It also scales very well. Indeed, this passive will be one of the main reasons this build works very well. It's synergy with the other abilities will be explained at their respective sections, in order to keep this one rather light.

Dark Binding

This skillshot will often define your gameplay significantly. The damage is decent and the control has proven to get very easy kills and assists for your team. Its range is tremendous and it actually just needs to scathe the enemy champion to hit, so its range is slightly longer than indicated and a little bit wider. The only downside is the high cooldown, which could be taken down a second or two imho.
EDIT: the 11/08/2011 patch took down the cooldown 1 second. It's still long but way better.
Still, because of these awesome qualities it is a skillshot which can hit minions as well, which means you need to learn to use it and get very experienced with it. Expect the unexpected and anticipate movement or abilities. Often, excelling with this skill is a necessity to be even a mediocre Morgana, let be a good one. Just like Blitzcrank, Lux etc...
It is very versatile in its uses, which I will try to enumerate below:

• Initiating. Often enough, a successful hit of Dark Binding start a teamfight, especially when you hit a champion that's not tanky. When it looks like you're going to have a teamfight soon, spam it like hell and aim it carefully. Try to nail down that one fed carry or nuke so your entire team can jump him. Landing one of these often already wins you the teamfight.
• Harassing. It can be used in lane to harass your opponent, but I do not advise it. It's a skillshot and often you'll want to hold your mana back to farm with your Tormented Shadow. If you want to harass someone in lane, follow it up with your soil on a successful hit, but don't do it too often if you plan on staying in lane for very long. I usually only do so when I expect to be able to take a tower soon or force the harassed champion to recall.
• Ganking. Much like initiation, but landing the first hit becomes vital. Often when being ganked players pick up a very predictable movement pattern towards the nearest allied champion, bush, tower, ... You'll get to predict this the more you play. If you're unsure about the movement pattern of your target, you can flash to end up closer to him for a sure hit. You can avoid hitting minions this way too. Still, try to be experienced enough to land a hit without using up a flash.
• Escaping. As with ganking, but try to hit enemies at the most opportune moment. For example when a snared enemy will block off other chasers, when he just used a gapcloser, when you desperately need healing through your spell vamp or when an allied champion comes to your help and you want to punish them for overextending. It's all about timing.
• Checking bushes. Only if you got the mana for it. This works because you can see your bolt disappear on a hit. If your know your range, you also know if it disappeared too soon. Follow a hit up with your Tormented Shadow, simply because it's fun to troll gankers.
• Farming. Try not to. I sometimes do it to get the siege minion in a quick go, but definitely not begingame.

Again: skillshot, learn to use it.
It's synergy with Soul Siphon is decent because it lands you a pretty good amount of health, so you can use it on minions when you're low on health and afraid of a roaming towerdiver.

Tormented Soil

This'll be your main farming ability. Note that it also reduces the magic resist of your targets by a decent amount each second. Unaware enemies can find themselves raped by this reduction if they stay in it for too long during a teamfight. Aside of that, combined with Rylai's Crystal Scepter it instantly slows a whole group of enemies, giving you an addition controlling edge.
EDIT: The 10/08/2011 patch lowered the mana cost significantly, which removes several mana issues.
It's area is quite large, so you can whipe out whole minion waves from its level 3 by popping it between the caster and melee minions. In a teamfight you can also usually pop it under three or more enemy champions, preferably beneath the melee scene.

Generally you use this ability to follow up a hit of Dark Binding to ensure your soil gets some hits in as well on the snared target.

As for your spell vamp, it's synergy is amazing. You'd say the 33% effectiveness of it because it is an area spell is rather poor, but the rewards are still huge. You can easily regain half your health from a single minion wave. Since it's also damage over time, you can pop it at the start of a teamfight and reap its rewards over its course, so even when a carry targets you you can keep going on several seconds longer. I often use it on a minion wave when I'm getting ganked, so I'm sure to receive a good amount of steady health while running away.

Black Shield

Don't start a lynching party here, but in my opinion this ability on its own makes Morgana a champion worthwile of having on your team. It is one of the most underestimated abilities, since people like the entire nuking much more than the support. Fact is, however, that being able to ignore any magical effects is so incredibly awesome people should build a shrine just for it.
Use it to:

• Protect your carry. Like any support, pop it on your carry always. Most people respond to enemy carries by controlling it with stuns, snares, silences, ... but this shield effectively gives him immunity to all that. Not only does it not control him, the controlling ability is still spent (unlike Kayle's Intervention that simply makes you untargettable). Since controlling abilities usually don't do very much damage, the shield itself can absorb at least three of such. The damage it absorbs is just sweet bonus gravy. Note that when you really get focussed down and the shield is knocked off, the control protection is gone too, so don't get cocky.
• Checking bushes. Most players have the habit of throwing their control first when ganking someone, so popping your shield when facechecking a bush makes sure those abilities are useless. Moreover, since they just spent them, escaping is easy. Preferably still use it on your tank and don't facecheck by yourself at all, but it is an option.
• Escaping/ganking. Nearly guaranteed escape or flawless chase.

No synergy with spell vamp at all, but what did you expect?

Soul Shackles

Morgana's ulti. Nice to get some instant damage with an additional hit of damage and a stun after a few seconds, but kinda like Nunu & Willump's Absolute Zero. It's huge damage if you can keep people in it long enough. In teamfights I usually nail down about two champions with it, mostly because you should already drop two in those four seconds before the ulti ends. Still, when you do end it successfully, you've hit a sensible mark.
EDIT: The 10/08/2011 patch reduced the secondary effect's timer to 3 seconds instead of 4. You'll hit more often now, but the stun is a flat 1.5 seconds now instead of scaling.
Use it to:

• Finish someone quickly. If you find someone at low health, the instahit aspect of this ulti will net you the kill without any delay. It's useful to finish someone off when you know his teammates are nearby, but it costs you an ulti.
• Escaping. The idea is that if they chase you with your ult on, they'll get stunned and you'll escape, and if they leave the ult's zone, you'll escape as well. So if you reckon you'll manage surviving the whole four channeling seconds, this is a guaranteed escape. But again, it costs you an ulti. Try using your Dark Binding first, and only your ulti if the need is high or you need to escape multiple chasers at once.
• Initiating. While this improves the chances you'll end your ulti before the teamfight is already over, chances are you can't target the squishies, you are controlled yourself (as in a knockback) or you're focussed down. Unless you're confident of your abilities to stay alive, don't do it ever.
• Chasing. Don't be afraid to use your flash if you think he'll break the shackles. Ending this ult nearly almost gets you a kill or assist when you chase.

So when is this ulti useful, if almost every option is yellow? Well, as I said, it's used best in a teamfight right after your tank has initiated. No special fancy tactics, just the downright "spam all my abilities and do damage".

Chances are that you're going to get focussed down when you pop it, because people don't like your ulti ending. Building and using Zhonya's Hourglass right after your ulti has been activated saves you 2 seconds. The spell vamp should keep you alive for the rest of the trip. It also slows your enemies somewhat, which is a nice bonus to control, but it's not that tremendous. With a Rylai's Crystal Scepter, however, it becomes quite good and increases the chances that your targets can't escape the ulti quite significantly.

Speaking of spell vamp, the synergy with Soul Shackles is decent to poor. Fact is that you usually use your shackles only when you're not that damaged, so the spell vamp gets wasted. Even more the second hit of the ulti does not give spell vamp. So don't count on getting healed for a second time when it ends, because it simply doesn't.

In general

There are many more uses of the abilities, many more item synergies, etc... These are the most prominent ones that you'll need the most. Again, playing the champion and gaining experience is better than reading a build and memorizing a theoretical tactic.

I often use my powers rather aggressively, because my build is very survivable and beefy. Just take note that your cooldowns (even fully reduced) are higher than 6s and the mana cost is rather high, so you can't just spam like a maniac.

I'll discuss my own item picks and some good alternatives now. Situational items will not be discussed, since they are plenty and each item is decent is some kind of situation.

Will of the Ancients is awesome. I've heard the arguments that it's useless since Morgana already has this item inherently due to Soul Siphon and it's better to pick another one that concentrates on another field of interest. I disagree, you should accentuate your strong points. If I get 35% spell vamp for free through my passive, I'd say hell yeah to 60% if it only costs me one item. This item alone makes you nigh unkillable begin- and midgame. Furthermore, it's a good support item. Your whole team will be thankfull for the free 25% spell vamp aura.

Ionian Boots of Lucidity is a solid pick due to Morgana's cooldown problems. icon=Sorcerer's Shoes is only decent, since you already get a nice magic resistance reduction from your Tormented Shadow.

Rod of Ages is a standard pick for Morgana. The combination of mana, health and ability power outperforms many other item options. Only a Rylai's Crystal Scepter is able to compete in my opinion, which could save you an item slot for a situational item.

Rabadon's Deathcap... Obviously.

Zhonya's Hourglass. A solid choice because of the synergy with the ulti and a decent ability power and armor boost, but it is often better to replace it with other items like Abyssal Mask or Void Staff. It just depends on how you're doing. I like Lich Bane as well as it adds that extra punch when you've spent all your cooldowns, and it helps farming.

Rylai's Crystal is a very decent choice as a last pick since it has very good synergy with both your soil as your shackles. Besides, no one sais no to more health and control...

The skill sequence is rather standard. You try to level your farming skill Tormented Shadow the fastest while picking your ulti Soul Shackles whenever you can. Try to keep at least one level of Black Shield in your abilities as that's already sufficient to reap the benefits of its control immunity. Level your snare Dark Binding as a secondary ability to your soil.

You can obviously deviate from this sequence, for example when your lane opponent has few control and does few magic damage it might make more sense to hold off levelling your shield at all. This is also an option if your opponent is a very heavy pusher like Mordekaiser, since you will have your Tormented Shadow at level 3 one level sooner, which allows you to push harder than him. Then again, with a very aggressive opponent that likes to harass, you might want to level your shield as a secondary rather than your Dark Binding.

A small list of useful spells:

• Obviously. I never leave home without it. Morgana is slow, so this makes escaping or chasing so much easier. She can also flash into a teamfight and Soul Shackles everyone in one go, or flash towards a running enemy to make sure the ulti ends. A nice kill I tend to make is snaring someone through a wall, putting my zone beneath him and if I think I can get him fast enough I flash in and ult him, netting the kill instantly.
• You are a semi-support. You don't really need it to be good yourself (like Lux or Ezreal), but it helps the team like hell.
• This is an awesome summoner spell to have that enemy carry do only 30% damage. As a support it is very useful.
• Indeed, Clarity. While it is often put in the same bracket of sucky-ness as Heal, I feel that for a support that is so terribly mana intensive, it still scales pretty well and doesn't impose a huge debuff like Heal. It's an area support spell and often I find I can use it to help some teammates and myself get back in there without having to recall or hogging blue every single time. It restores about seven ability uses, so it's really useful when you're down a bit.
• It is very useful to defend a tower or gank an enemy. Particularly useful for Morgana as she's indeed able to whipe huge minion waves in a matter of seconds and even hold off three enemy champions under a tower.

Pick what you like best. Also Ignite has it's obvious merits. I prefer Clarity because I like to lean towards the support role more and I tend to play aggressively begingame, making my mana deplete rather fast. It's a personal choice that I know some will not agree with, but it works very well with my playstyle.

As I said before, your functioning will be vital to the success of your team. Unlike a carry that can have a "right-click to win" mentality you need to employ several tactics and have a good understanding of your abilities. I often find Morgana very decisive when you land a good Dark Binding or Soul Shackles.

You will need to accept that your role and life is secondary to the other members of the team (except the tank). You are a nuke, yes, but also a support. There will most likely be a better mage (like Brand, Karthus, Annie, ...) mid that'll do a way better job at nuking than you with way lower cooldowns.

As for the blue buff. As I said there'll most likely be a better mage that needs it more. However, a buffed Morgana will literally rape. You will want to take it whenever your team lets you.

On a more tactical note:

• Spam your Black Shield on your carry or the focussed champion of the team. Save lives, win teamfights.
• Use your Tormented Shadow to soften up the entire enemy team.
• Try to Soul Shackle as much enemies as possible and especially the squishies.
• Dark Binding should be used on predetermined targets and with plenty of skill to get the most out of it.

In general, this build is all about survivability and being a good team player.

You will mostly get assists. It's not very common that you'll be the most fed champion on your team because of your semi-support role, but there are other champions for that purpose. Mostly I get Medium/Low/Very High stats for Kills/Deaths/Assists (10/3/25 for example) and get most of the money I'm missing out on kills through Morgana's excellent farm. You'll miss out on kills especially in the post- Will of the Ancients pre- Rabadon's Deathcap stage, where you'll lack just that tiny bit of finishing power.

I generally also score about second most "money earned" as well as "damage dealt", so don't assume this build's focus on survivability has impaired your ability to perform well as a nuke. Your ability power should hit nearly 500 and your scaling is pretty good, so you've got enough sugar to spice up the fight.

Remember to read other guides and builds, and especially to learn by playing.