Summoner Spells:
Ignite to help finish off what you've started, it also helps against healing and spell vamp characters.
Flash is a good escape for annie, the only thing remotely close as an escape for her is her stun, and her molten shield so it helps with her utility.

Mastery Tree:
21/9/0 maximizes dps while giving some survivability. You sacrifice Mana/Mana Regen for hp. If you are last hitting correctly there shouldn't be too many mana problems.

Skill Sequence:
This sequence will maximize your laning phase. 1 point in shield to help increase the interval in between stuns.

Rune Build:
Flat Magic Pen Marks - the item build i chose for her rushes magic pen and resistance reductions, these runes help for a good start.
MP Regen per level Seals - Nothing in this Annie build has mana regen, I find that these add the perfect ammount of regen late game for my play style.
AP Per Level Glyphs - Great mid to late game damage boost!
Flat AP Quints - Great beginning to mid game damage boost!

Items:
Starting items - I choose boots and 3 pots. Annie is at a disadvantage with range on her q, I find boots give her the upper hand on speed and allow for weaving in and out to last hit and harass. 3 pots give her lane sustain at the beginning.

Beginning Phase - Upgrade to sorc boots and get an abyssal scepter. If you are mid you will most likely be fighting another mage type. With this beginning combo your spells will cut through almost all of their resistance, and give you resistance and speed to cut through them and take some hits.

Mid Phase - Next get a needlessly large rod, and then a catalyst for dps and survivability. Upgrade the rod to rabadons, then the catalyst to Rod of Ages. If you get to this point in the game you should be hitting like a truck.

Late Phase - Next choose 2 out of these 3 items based on your situation. If you find that the other team is building magic resistance to counter you, purchase a void staff. If they are AD heavy and you need that extra 2 seconds in fights, get a Zhonya's Hourglass. If they are AP heavy and you keep getting stun locked, get a Banshee's Vail.

Of course play around with different builds, it all depends on your play style and who you are facing.

Game Play:
At the beginning use Annie's q to last hit. If you bought boots first there's an 80% chance you are faster than you enemy at mid, use that to your advantage to stay out of range, last hit, and harass effectively.

When you hit level 6, you officially have enough burst to scare/kill people. build your passive to 4 stacks, start running in and pop your E then Q. While stunned pop W, R, Ignite! If they aren't dead they are running. If you have been harassing then wait until they are at half health then pop your combo for a guaranteed kill. If they have healing abilities then pop ignite when they get out of stun.

At level 8-10 team fights will be starting. You want to use the same tactics, but AOE stun in team fights. That's a game finishing move if used correctly.

At level 15 if you are doing well then the other team will be countering you with MR. Get a void staff, and make sure you are popping bubbles before sending your stun out. think ahead.

At level 18, choose your fights and items wisely. Annie is a great late game AP carry, her only downfall is that she is squishy as ****. you HAVE to get the drop on people in order to win fights at this point in the game. If you find yourself to squishy purchases the corresponding item listed to help with the situation.