Annie can be very powerful, if used correctly.

Firstly, you need first blood, especially if you are mid. To do this, harass them with your auto attack, and charge up your stun by lasting hitting minions with your Q. Then, once you are level 6, flash in, use your ultimate on them, w, then q, ignite, then an auto attack, then you've got first blood.

If they are just out of the range of your ulti, you can use it right on the edge because its area of effect, if you have charged up your stun, you can ulti, then w and q, and you've got another kill even though they nearly escaped.

You can also use your E, Molten Shield to charge up your stun, but I really wouldn't bother getting that skill until you've maxed at your other ones first.

OK, so two of Annies skills are AoE, so, you can stun their entire team with your ult.

Wait for your team to go in first, try to make them close together so you can get an easy stun on all of them. Then, flash in, ulti, and then w, then you've most likely got 3/5 of their team on half or even killing them if your well fed. You'll win every team fight this way.

Pros - High Nuke Damage
Able to stun the whole team
Easy to play

Cons - Very Squishy
Slow
Relies on ult to kill most people

The runes I have suggested are really needed for Annie.

The early game domination relies on that extra AP you get from the runes, and the magic pen helps late game and early game.

The masteries I have suggested are normal spell caster masteries. The final utility skill is very useful, especially for Annie. Archaic Knowledge is also very useful, but it may be switched for burning embers as some people prefer

The items I have suggested rely on you dominating in the early game and not dying, if you think you will die a lot, then skip the mejais, and build a morellos evil tome insted. The combination of the mejais and Rabadons is unbeatable, early game, you'll have something like 400AP if you get 20 stacks on the mejais, and the rabadons.

I have suggested two rylais at the end because its so late game that its too late to get a Rod of Ages.

The Skill Sequence I have suggested is very useful, you use the Q at first to last hit and charge your stun, then your leveling up your W, which does the most damage out of Q and W, its also area of affect.

I have suggested the E skill at the end because I think its a waste to get it early game, and I doubt people will use it. You can however, use the E skill to charge up your stun.

The Summoner Spells I have suggested are very useful. You can use the flash for initiation or to escape. I am sure many people would be scared of you, so the flash really helps to catch up to people, or suprise them!

There are a few counters to Annie that you should be aware about.

Firstly, champions wise there are;
Veigar - Long range, and his ult allow him to kill any Annie with ease
Malzahar - The silence and the ulti (suppresses) allows him to kill you with ease
Le Blanc - Very fast, can jump in and kill you, but you can kill her as Annie, you just need to have extremely fast reactions

The only item that counters Annie well is Banshees Vail, this is because it blocks your stun, and seeing as you are quite close range, then they will resist your stun, and then stun/kill you.

There are many opportunities to get kills as Annie.

For example, if you see one stray off from the main group, just flash in and kill him.

You will alos have opportunities to kill their entire team, again you can flash in, if they are in a group, you nuke them all to hell, then hopefully get 2 or maybe 3 kills out of your nuke. You can then run off and let your team finish the job.

In affect, they were about to push the turret, and they died for it.

To be quite honest, if you dominate ingame as Annie, you won't need any more items then 20 stacks on Mejais and a Rabadons Deathcap. This is because, you nuke them so hard, even if you half health them, your team will come in and finish them off.

If you really are low on farm, you can kill the jungle with 4 creeps in it, the one next to mid lane. A W on them will kill them all instantly. You can also use your W on minions waves, but I would only do this if there are a large amount of them, and your at a safe distance from the opposite team.

It is also better, especially with Mejais to just go around ganking and getting kills, you will get more money from kills as well, whilst killing them, restricting them of farming for a while, which helps you and your team.

The conclusion of Annie is that, she can be very powerful if used correctly, but many people use her wrong. Her stun and AoE damage helps considerably in team fights, but it must be used correctly.

Annie may be very hard to play at first, but once you learn her, shes very good, to take advantage of the opportunities that the opposite team give you to get free kills.