Abilities

Passive
Death defied This passive is what makes karthus who he is. Many consider his ultimate as his most important ability. In reality this is what makes him a very good pick and this explains why he is still frequently picked in tournaments. Being able to stay alive for 7 seconds and not be interrupted is amazing. This is why positioning is vital for karthus: you can't move when you die. In teamfights the aim is to find the perfect spot to die in.

Q spell
Lay waste Karthus' primary damage ability and his most important skill-shot. It grants vision in a small area on a 1 sec cooldown, very useful for level 1s. The damage may seem small but on a single target it deals more damage than most primary damage abilities ( Lux's Lucent Singularity, Twisted Fate's Wild Cards etc...). The 0.5 sec delay forces you to "lead" your target, aiming in front of their path. It happens to also be your primary farming tool, karthus having the worst AA animation and lowest ad in the game.
tip: while farming, try to aim it so it only damages 1 minion, dealing more damage and not pushing the wave too much.

W spell
Wall of pain your only CC ability and a quite useful one. The slow really helps landing Lay Waste and can even serve as an engage tool in the late game. Use it in any engagement to disengage, engage, or just to lower the movement and magic resist (very useful in trades and overall to deal additional damage). Also note that the obelisks of the wall grant vision, not the wall itself.

E spell
defile This spill grants mana sustain in lane passively so you don't run out of mana using Lay Waste to farm. More importantly it is your most important skill in team fights and objectives. The damage may seem small once again but it is AOE and per second, making it stack up very quickly. In team fights this ability must be turned on at all times and you must try to hit a maximum amount of people with it. In the laning phase it should be turned off unless you want a lot of extra damage and to be OOM extremly quickly, the mana cost being high.


Ultimate spell
Requiem. Karthus' ultimate is his most famous ability. Being able to damage champions regardless of distance is huge: just press R to get penta. Play Video (note: this is not my video, the video was made by user mdradde09 and is his property)
Of course this ability is much more complex and there are several situations were one must not press r.

Golden rule:: NEVER PRESS R UNLESS DEAD OR PERFECTLY SAFE.
Requiem has a very long cooldown and if interrupted does not refund the cooldown. You do not want to be in this situation

Karthus losing the teamfight on a silly mistake.
That requiem could have at least got a kill or 2 and maybe turn the fight around, but instead it led to a 4-0 exchange.

When to use requiem::

• To secure a kill that noone can get. The most famous use, finishing off a low health enemy that no-one can kill. The numbers to remember are 250,400 and 550 health. Try to wait for an enemy to be below these thresholds and make sure they don't have a life saving ability (shield, heal, unused untargetable ability etc...)
• In team-fights when dead. The other use is to not make the previous mistake and to wait to be dead in Death Defied to channel Requiem without being interrupted. Be careful to not wait too long before channeling, other wise you won't be able to.
• taking a inhibitor turret One way to stop a standoff at the inhibitor turret is to use your ultimate to damage the enemy team. Either they go back to heal which allows you to take the turret or they stay at the risk of being engaged upon at lesser health. Only do this if there is no other way.
• When 2 or more team mates are in a engagement without you.This is the one that requires the most judgement. When you see an engagement at bot lane for example if the fight seems to be even use it, it may turn the tide in favor of your team.

In comparison don't do the following

• Use it to kill steal.
  
  Just because an enemy is killable with Requiem does not mean you should use it. Usually the enemy champion will die in the following seconds thanks to teammates. Only use it when it is 100% guarantied to not kill steal (unless its a team fight)
• In an lost or won engagement not involving you. If your team is clearly winning or loosing the engagement then it's pointless to use it, the kills are either guarantied or the opponents are too healthy, making it a waste

Skill sequence

Ability Sequence
1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18

> > >
We max Lay Waste first for the damage and easier farming ability. It's also very useful for level 1 teamfights with the vision it grants.
We max Defile second for the mana sustain and damage in skirmishes.
We max Wall of Pain last because it is a utility spell.
We always take points in Requiem at levels 6,11 and 16

Alternative set up: it is entirely acceptable to take a second point in defile at level 5 for the mana sustain. Do this only if you have trouble managing karthus' heavy mana usage.
Moreover if you are quite good with Karthus' mana usage you may consider taking additional points in his Wall of Pain post level 7. This depends a lot on if you get blue buffs or not.

Runes and masteries

• Greater Mark of Magic PenetrationX9: Standard marks for an AP mage, lets you deal some damage early game. The only real option in Marks for Karthus.

• Greater Seal of Scaling HealthX9 Good runes for additional survivability in the late game, which you will desperately need. The best runes in most circumstances
• Greater Seal of ArmorX9 These runes are very effective against an Ad mid to avoid falling behind too quickly.
• Greater Seal of Mana RegenerationX9 These seals are only if you have trouble managing your mana. a decent alternative but not the best

• Greater Glyph of Magic ResistX9 These glyphs are perfect against most AP mids and give some survivability for early game. They help Karthus survive the early game where he is at his weakest against AP Mids.
• Greater Glyph of Scaling Ability PowerX9 The alternative set up is more offensive but grants quite a lot of ability power at level 18. The best set of runes when not facing an aggressive Ap opponent

• Greater Quintessence of Ability Power Quite explicit, gives more AP for Karthus, nothing else to say.
• Greater Quintessence of Movement Speed These runes are quite useful if you don't want to start boots and are facing a skill shot heavy champion. Moreover they are quite good to help you get into a better position in teamfights.
• Greater Quintessence of Spell Vamp these quints are quite niche but can be useful if taking Hextech Revolver after Tear of the Goddess. You'll have mana and health sustain from the start. Useful depending on playstyle.

Masteries

Item build: the classic way

• X4 X2sight ward
  A very standard start that provides health and mana sustain as well as starting to build Tear of the Goddess. The ward also allows you to avoid certain ganks and to play much safer. The recommended start for 90% of the cases.
• X5
  This is highly recommended against an AD mid to survive the laning phase, especially considering the lack of armor karthus has in the early levels. You will need the additional armor to survive but you can substitute a Health Potion for a Mana Potion to alleviate mana problems.
• sight ward
  This start provides less sustain than the first but if you are forced to back a lot it will be better. It is also much better with teleport as you will be coming back to lane faster. In short this start is better in a poke heavy lane or if you roam a lot as Karthus
• 
  This last start has the least health sustain but actually gives quite a lot of mana sustain. It synergises well with Defile's passive and allows you to be quite agressive. Plus the extra health can save you against some high burst champions.
• X3
  The season 2 start that was heavily nerfed in season 3 is still useful, just situational. the added mobility is quite useful in certain match-ups against skill shot heavy opponents ( Brand, Lux...)

• Since the tear nerfs this item has returned to it's core status. Not only is it good for the health and mana sutain is gives, it more importantly makes your mid-game far better than a tear start. Should always be rushed unless special circumstances. The health, AP and mana it gives are too good.
  
• : This item was core on Karthus until the tear nerfs. This means you take more time to stack it and this is crucial. Because you are essentially waiting for it to be useful you have invested 700g into an item that will repay itself 15 min later: not ideal when the game is fast pasted. Moreover with the meta shifting heavely into Mid lane assassins taking a tear first back is very dangerous. If you are against a safe lane you can still take it. Don't forget the item itself gives 90AP (60 base, 30 from passive at 1000 mana) and a very good shield which essentially works like Barrier: it protects you for several additional seconds. Also don't forget it would give 3% of 2818 which is 54 additional ability power. A very late game oriented choice.
  Important: both of these items are key to maintain Karthus' heavy mana costs. If you fell you are in a safe lane and can farm well or if you are ahead in kills, take both. If not then stick to only taking RoA, the tear delays your build too much.
  
• : As Karthus you want damage and this item is the best for that. 120Ap + the passive will make you hurt quite hard. Karthus really becomes threatening after this item is completed. Core item but don't neccessarily rush it after your mana items.
  
  
• : This item is the last core item for 2 reasons. Firstly it gives a nice amount of AP ( 120AP) and armor. the latter is very useful when going against the enemy AD carry. But more importantly it gives the active statis. Not only does this give you 2.5 sec of invulnerability, it gives you 2.5 sec of free damage in teamfights with your Defile. It is a must have for the survivability it gives in Team fights.

These boots are the best on Karthus just for the magic pen they give, very useful to deal additional damage.

The best defensive boots, should always be taken when struggling against an ap mid laner. The tenacity is also nice against Crowd Control that would hinder you in team fights (like Lux's Light Binding, Veigar's Event Horizon...)

The most situational of all 3, should only be taken if the enemy Ad mid laner is problematic and/or you are against a full Ad team

Most of the time you want to take Enchantment: Homeguard as the others don't offer much. If you take teleport you may try Enchantment: Distortion or Enchantment: Alacrity when you need the extra MS.

As of now it seems the only interesting trinket is the Stealth Ward for the free ward. The other 2 are not really suited for Karthus as neither correspond to his gaemplay: you don't need to snipe people with the Scrying Orb and you are not suited to ward hunting with the Sweeping Lens.

• This item is very underrated on Karthus. The penetration compensates for his poor Ap ratios and the burn is quite powerful. You deal 2% of currennt health (which equates to 1% of max health per second on average) which refreshes for every tick of Defile. Essentially you do a lot of extra damage per second with it. hauting guise also boosts your mid-game but should really only be taken when you need AP and health and the enemy has not much MR. Otherwise don't. .
• The other underrated item on Karthus, it gives survivability and a decent amount of AP. The slow is also very interesting. While you'll only get the Aoe effect, it still allows you to kite very effectively and prevents people from escaping your Defile. It pairs up also very well with Liandry's Torment to double the burn effect.
• A decent AP item that, while providing some damage and penetration, also helps against AP teams. A must have against a double AP comp and a early Negatron Cloak can really save your laning phase.
• The best Magic penetration item. With the nerf to magic resist getting this item will make you do near true damage. Should be taken if the enemy has more than 100 MR. (note: it does not go well with Abyssal Mask, reduction being applied before penetration).
• The new will of the ancients is an item you would only get if you need sustain immediatly. It costs very lttle but does not provide much. It is best to leave the Hextech Revolver non-upgraded as 2000g dealys too much your item build.

Gameplay: Early game

Karthus

• Farm This one is fairly simple but essential on Karthus. You need items to be powerful and you'll mostly get them via farming. Your goal is to get around 200 minions at 20 minutes. The minimum should be 175 otherwise you should consider going for the back-up build (not taking both mana items). Keep in mind that a kill equates to approximately 15 minions. If you have trouble getting this score go practice in a custom game.
• Help your team out. This one is more complicated. Essentially you should always prioritze helping your allies over farming. Many players fall into the Nasus syndrome of afk farming till 20 min. Don't do this and help your team in any way possible. This becomes easier with Teleport.
• Play safe and don't die This one is the hardest but essentially you should try to not give any kills, even if it results in a 1 for 1 trade. You want to farm and dying only sets you back. Moreover you don't want your enemy snowballing out of control. Don't overextend and try to follow this to stay safe

Warding

There is however a big question that is often asked for Karthus:
Should Karthus try to be aggressive in the early game?
In my opinion Karthus should always try to poke the enemy mid laner. Some opponents think the lane will be easy and not expect the poke. Moreover you can do quite a lot of damage should you hit several single target Lay Waste. If your ahead then definitely abuse you advantage and poke. If your behind then don't poke so much, try to be passive. Sometimes you can win entire match-ups just by landing a few single target Lay Waste in the early levels. You can even try to punish players and go all in if you manage to land you skill shots. Just be careful.

Detailed level by level guide:
[*]Levels 1-2 This is the most important levels of the laning phase. You can literally lose the laning phase in these levels. Ironically Karthus is quite good here. Most champions at this stage have their main damage spell on a long cooldown. In contrast Lay Waste's cooldown is 1s. You should outrade most champions with single target spells. As such you can in certain match-ups be aggressive to gain an advantage and have a good laning phase. but be careful of certain champions with stupid early games ( Karma, Riven.
[*]levels 3-5 Here you still retain your advantage but now the enemy has their full combo up. Be a little more careful as ganks will start to happen around this period.
[*] levels 6 and onwards The enemy mid laner now has his full combo while you have requeim. Your focus should now be on farming as you need items to be relevant. watch the map, play safe and if you have not started already start to farm the jungle when you pushed the minion wave to the tower (which you also should start doing as you now enter power farm mode).

Teamfights with Karthus

• Jumping in the middle of the enemy team:What most players do in teamfights, which is the most simple to comprehend: you want to maximize Defiledamage by hitting as many people as possible. This is what karthus aims to do in most cases as it is essentially his role. This is especially the playstyle of Suicide Karthus.
• Waiting behind the front line, just in defile range. This is a more defensive approach that focuses on using Lay Waste on the closet target, sort of like an Ad carry. This is better if you want to also protect your Ad carry. This strategy especially useful against a kiteable team who has to walk to your back line. The tanky set up should use this strategy, especially considering the burn + slow effect.
• mix of both.This is the most used one that is maybe the most effective. You start out quite cautiously then when you see the opportunity you dive in, using flash if necessary.
• Going for the Ad carry this is quite simple: if you see the enemy ad carry out of position, abuse it! With Exhaust you should out damage the ad carry and your sustain damage should either kill him or make severly low. Also you may attract the attention of other opponents trying to protect the Ad carry, who will go straight in your Defile.

Solo queue and ranked teams with Karthus

Solo queue

Requiem

Ranked teams