I just made this as a build, but I would like to give some tips and all, now that I think about it, for when you use this build especially, but some as Annie in general.

All these tips upcoming were really for my friend, the original build was for me but I lent it and some tips to my friend who was just joining League of Legends and liked Annie.

I started this game with an almost exact (masteries and runes have been improved since) same build, and got First Blood. I was mid, and by the end I had got over 600 AP with full build, around 2500 health, we were winning pretty easily, pushing with ease, blue buff and Baron encircled around me. I got a triple kill later. My end score (we won, btw) was 21/9/9. I just wanted to share my experience with this build. I would've been 21/7/9 but I got cocky and died twice. Also, I got ksed 4 times, so if this hadn't happened my score would've improved to 25/7/5, but enough complaining.

1: Buy any items that build into your later items, especially the ending items.

2: Use your E when fighting minions from time to time, especially super minions, if you want, and also use it to get closer to your stun.

3: The best time to use your stun is if you have Tibbers ready, or better, use it FOR the stun. If not, use your W or Q, better your W in a 2 or more enemy engagement since it allows you to stun more than one person. In 1v1 or more for you against them, use your Q to stun.

4: Try not to waste stuns on Dragon or Baron; it won't work. You still can, but try to use less abilities for attacks unless you have a shortage of people there, or you are soloing. Best outcome in my opinion, you build towards your stun so you can use it instantly against your next enemy.

5: Don't be afraid to use Tibbers to tank Dragon or Baron or a turret. Just avoid it, and don't use it if the target it full health, make sure they are low almost half health, or with a turret, you can pop him before that.

(This is pretty much for every champion except for supports)6: Chase until the enemy gets too close to a turret (unless they are low and you have enough health to keep it up or can get away before either can kill you) or too close to a champion who can kill you, judging by you, the enemy, and him.

Also:

You can replace your Rylai's with a Rod of Ages and your Will of the Ancients with a Archangel's Staff, but if you do you MUST RUSH YOUR ARCHANGEL's STAFF, as rushing your full boots is not good. You also want AP quick, so it is a good choice. This different build, however, WILL lower your end AP to 624 and some other things will change as well, though no matter what build you do, the Shoes and Deathcap are CORE ITEMS and are *needed* for Annie and a lot of other AP champs, as they increase speed and MP and give you 120 AP along with the 30% of your AP bonus.

If you are 1v1ing an enemy champion, by all means, rush your stun and pop everything, but wait to pop your E until they are out of your stun, and auto attack when you can't use an ability.

Just by the way:

The ending AP for the first build is 637.

Referring to my earlier tips, just use your Q and W a lot, and your E when under attack. Use your Q mostly for your stun since you can't miss, and use W for possible ganks, from you or from an enemy, along with E. Use your R after a stun, or if more than is there, for the stun, but it is probably most effective during a stun because it provides an easy target.
Pick off minions with your auto attack, W, and E.
Tibbers makes laning a lot easier, especially at level 11 and above.

Use your Q to get one person down quicker occasionally, but focus it only if your team tells you too or someone comes too close and alone, or at least mostly so.
Use your W when people are close, or to pick off annoying minions. With more AP, it provides a lot of damage, and it stuns multiple people.
Use your E when under attack, or being chased. You can also use it to get to your stun quicker, or to pick off minions faster, as stated above.
Use your R when people are close, use it as a stun or after one for maximum effect and damage. You CAN also use it to scout or to tank for you if you push a lot, also stated above.

This has been my guide on Annie. I hope you follow this build and its tips (maybe not the runes :P) to help you become better at Annie, and later all of League of Legends. If you find something shouldn't be here or should be improved, by all means do what you feel should replace it, test it, and then discuss if you found the change better than the original. Thank you for reading this guide :D