Good question!
As the years go by, support is becoming more and more popular.
But as a role in a game like league grows in popularity, the quality of that role decreases in response.

I'm here to offer the information I've learned up until this point, and I've been playing the game for two years or more.

Who are you and why should I care?

I'm nobody! And you shouldn't!
Glad we could get that out of the way. :)

I feel Lulu is overlooked as a support, and she really shines in the role.
It only makes sense because she was released as a support afterall!
She's also one of my favorite champs for the position, and with my experience with her it makes it much easier to explain how she works to others.

Tl;dr I want to help people learn support and I figured I'd start with my favorites first

I am too lazy to put champion matchups on the other build page, as I assumed it would just do that for me automatically.

Current Patch: Preseason 5

(I will update this as things change)

I'd like to start off by saying Runes and Masteries are what you feel comfortable with, people trick themselves into thinking they need to run 100% what they see and that's not how it is at all.
Some runes and masteries work better than others, as say, running a full crit rune page on lulu wouldn't be as efficent as running a full ap page.
So if you use common sense and think about what you need for your role you should be able to figure out what works well.
I'm just going to discuss my two choices for this guide just so you understand why I chose them.

Basic Support

Damage Support

Summoner Spells

+
This is the standard support combo, exaust can be used defensively and offensively so it's great and flash is METAGAME AHHHHHHHH

+
I only take this against heavy sustain, because Soraka is such a hassle.

You don't have to 100% follow these to get the most out of this guide, always do what you're comfortable with.

Early game is always a fun time in bot lane, bush control battles, ward battles, who can poke the enemy adc out of lane/consciousness first.
Ah potions are in the air!

GET OUT YOUR RELIC SHIELDS, YOUR SPELLTHIEF'S EDGES, YOUR ANCIENT COINS

(That aren't actually coins)

IT'S TIME FOR WAR

Lulu's early game is fairly straight forward but to make things easier on you I will explain exactly how you should play it out.

Harass

You should never Glitterlance constantly, instead use Help, Pix! to put pix onto an enemy and then Glitterlance them.
This spends a tiny bit more mana than you would just using Glitterlance, but it'll save you more in the longrun, Glitterlance is fairly easy to get away from if fired straightforward at a target.
It's more preferred to hit the carry unless the support is just letting you wail on them, or they're Sona.

Also don't forget! Help, Pix! Can be cast on ally minions (it doesn't shield them anymore) as well as enemy minions (it deals damage to them still, so be careful not to kill them).
This opens more windows to hit those pesky Carries like Caitlyn or Varus

Whimsy and Trades

Whimsy is absolutely beautiful all around.
It offers: a decent slow, a potent disable, and it can function as a speed buff to get you or anyone else out of hairy situations.

I'll paint a picture for you;
Let's say Leona just Zenith Bladed onto your Ashe and Lucian is coming in to do some serious damage.
You cast Whimsy on Lucian and then you Glitterlance him to show him who's boss.
Leona continues to be aggressive towards your Ashe thinking she needs to even the trade Help, Pix! onto your Ashe negating most of Leona's damage because she needs her carry to proc her Sunlight passive.

In this situation you would only cast Whimsy on Leona if Lucian didn't follow up to Zenith Blade.

Whimsy + Exhaust can almost be used to turn around any fight, as you can technically "disable" two targets instead of just one.

Hugeify!

Wild Growth is great for offense and defense equally.
It can be cast on a low health ally to give them a good chunk of health back to put them back in the fight or help them escape death.
It doesn't have to only be used for clutch butt saves though!
It can also be used on your team's initiator, and it can even turn Lulu into an initiator!

Warding

Warding is pretty strange since the changes to vision/vision items in season 3.5/4

I will make images for this later, as right now I'm just putting this together.

I feel like Middle Game or Mid Game as it's called is vague and never truly definite, some people think mid game is at 30 minutes into a game for whatever reason and some feel it's at 20 minutes.
I'd like to believe the standard time for a game is 30-35 minutes at the max (though most of us know this to be untrue)
So I'd like to say Mid Game is about 13-20 minutes into a game after several objectives have been taken (towers, dragons, etc.) and several people have at least one or two complete items.

By this point you should have Sightstone and Sweeping Lens for sure.
If you don't you are not providing your team with the vision they require.
You should also have either Sorcerer's Shoes or whatever choice of boots you wanted, as well as at least a Chalice of Harmony Or some other heavy mana regen item
If you don't then this is where it gets tricky.

We're getting #WrEkKkKt what can I do?!?!?!

Don't panic, this is the make or break time bud.
First off look at what your team needs;

Is your Marksman/Adc Falling behind? are they d/c? did they get mad and start feeding?
Is your team severely lacking damage because of this and because the other lanes didn't do so hot either?

TIME TO BUILD DAMAGE AND DESTROY PEOPLE

Is it only your lane that's behind?
Build a typical armor defense item, and focus on utility and peel for those who are doing well.

Did a lane(s) snowball out of control?
Build defensively against what's really strong on the enemy team, focus on heavy utility to help your team escape/engage on people caught out.

Hopefully you can turn around this uphill battle, and recover.
If you can't, don't let it get to you.
You can't win em all.

Teamfighting

Mid Game teamfighting is just as important as Late Game teamfighting, aside from the whole "throw" aspect that Late Game has.
You may or may not use Glitterlance during a teamfight, it depends on what you need more of: Damage, or Utility.

Who to Whimsy: Anyone who can burst that jumps on anyone you need alive on your team
( Katarina, Akali, LeBlanc, Fizz, Zed, Etc.)
OR
Anyone who can provide heavy utility to the enemy team that jumps into your team
( Amumu, Jarvan IV, Warwick, Leona, Gnar, Etc.)
OR
Use it to speed buff an ally to catch a target/Use it to slow down an enemy caught out away from his team/Use it to disable an enemy who was caught out but has a good escape mechanic.
( Tristana, Kha'Zix, Ezreal, Rengar, Corki, Etc.)

Note: Whimsy does not work on champs like Master Yi or Olaf while they're ulting. I have tried to stop them from getting away or getting into the fight several times and it says immune every single time.

Who to Exhaust: Preferably Anyone who's fed/does the most damage on the enemy team, can also be used offensively to catch someone who got caught but may get away.
You'll have to make the call yourself.

Who to Wild Growth: This is also a call you'll have to make yourself.
During teamfights I always watch out for anyone who can be bursted instantly on my team, as you may have to peel for them with Wild Growth, but I also watch any tanky engager on my team because you could also cast Wild Growth on them once the enemy team starts trying to kill them to completely blow them out of the water, or in this case, off the ground.

What the heck do I do with Help, Pix!?
At this point in the game I find you don't really use it offensively unless you're the one who got fed or you have a lot of damage.
You should always use it in teamfights to protect people who are being focused.
It will also give you more chances to get a Glitterlance or two in while staying a safe distance from the action.

Warding

Vision is always important but now it's crucial to have vision on objectives like Dragon or Baron

I will make images for this later, as right now I'm just putting this together.

So it's Late Game things may or may not have been going so well up until this point, but you've made it, it's time to go up from the 30 minute mark until one team curls up in the fetal position and begs for their mom to pick them up after soccer practice because little Vi just punched them in the teeth.

WAR? WAR HAS CHANGED.

We haven't gotten a single dragon all game, what can I do?

What? Really? Ouch.

The enemy team has baron and they're pushing down mid!!!!!

Word of advice: Shut up, Kill, Kill, Kill.
Or at least lend your teammates a hand and help them fight.

OUR DUMB Master Yi KEEPS PUSHING TOP/BOT LANE AND WON'T HELP US!!111Zero!

That's pretty much his job at this point, just like it's yours to keep people alive and distract the hell out of the enemy team.

Joking/Question Statements aside, it's time to delve into what's left in the game.

You should have a full build at this point, or nearly complete, and you should be at least level 17-18, if not, better go kill some minions/camps.
You'll be using your active items more at this point in the game than at any other single point, because the decisions you make here are what are going to determine who dies, and who lives.

Late Game Teamfighting

Late Game teamfighting is pretty similar to Mid Game teamfighting, except losing a fight at this point (unless you're a decent amount ahead of your opponents) means a loss.
If anyone does something really dumb, like face checking a bush with 0 vision on the map and getting killed and it results in you losing the game, it's a Throw.
Them engaging when everyone was behind them a few seconds ago is not.
Don't say someone threw the game just because you didn't feel like going the extra mile to save them, because that's your job.
But don't get stressed, as I've said before, you can't win em all.

Who to Whimsy: By this point you should know who on the enemy team is making the biggest impact in fights, if they simply do a bunch of damage that doesn't have to be outright disabled then I recommend using Exhaust on them instead. You could save Whimsy on someone who brings more utility to their team at this point.
It'll be your call though.

Who to Exhaust: You most likely will use this summoner spell specifically for defense more than offense, you will always want to cast it on anyone who jumps into the fight and can output a lot of damage.
You will only use it offensively if your team is ahead, but if that's the case, why are you in Late Game?

Who to Wild Growth: You're going to use this on your squishies to save them from certain doom. Or if an opportune moment appears where your team can successfully engage and your tanky initiator is frontline, you can use it on them instead.

Help, Pix!?
DEFENSE DEFENSE DEFENSE

What about Glitterlance?
At this point you can use Glitterlance to clear waves of minions, or farm.

Warding

Objectives like Dragon or Baron are very important, but by this point it's anyone's game. So you'll want to make sure you keep vision where the enemy is going to frequent, or where your team needs it constantly.

There's no reason to make an image guide for Late Game warding because it's entirely situational at this point in the game.

I hope that the information in this guide has been helpful to you, and I hope that you start saving butts like I do. :)

If you have any questions or suggestions, feel free to leave a comment, or feel free to contact me in game.

I am currently working on a video guide for Lulu and it'll cover the same information here, except it'll show you more of Lulu's skills in action to give an idea of how to use them properly.