Hello there, Annie was my main and i thought why not make a guide for her? I love this champion cause of her nuke :)

Pros

A massive nuke
Two awesome aoe stuns
You got your own pedobear
Epic skins (most of them at least)

Cons

Easily focused if you're doing well
Not so good untill level 6 (when yo get ulti and do massive nuke)
Mana is a problem mid game (though deathfire grasp will help you with this)

I've chosen Ignite and Flash because ignite really helps you with your nuke.

and Flash as you probably alredy know you can escape incredibly good with Flash or chase Enemy team members easily.

I've put my points in offence cause of the 15% Magic penetration and some Cooldown reduction and a bit ability power. I put my point in Cripple (improved exhaust) because first of all, smite and crit chance suck on annie, and second cause you may remove ignite for exhaust but i strongly reccomend ignite for extra burst.

I've chosen Deathfire Grasp cause of it adds sick damage to the burst and some mana regen and AP of course. It's important to use Deathfire Grasp BEFORE you use any other ability because it does damage depending on how much health they got.
Rabadon's Deathcap because it's as you probably know very much AP.
Rylai's Crystal Scepter cause it give you the little extra HP and slow, and again of course AP.

Only use Void Staff some annoying bastard in the enemy team builds Magic resist. Else you can change it for a Zhonya's Hourglass.

You have to have stun ready for this!!

First you use your Deathfire Grasp, then your Summon Tibbers (ulti) and try to hit as many as possible with it. Then you use you're Disintigrate (q) and then Incinerate (w) and then use Molten Shield (e) for a stack on your passive stun.

Then continiue spam Q and W and you've pretty much overkilled them.

That's all i have to give you ;)

Hope it helps and see you in my other guides :D