Items:
Starting- Sapphire Crystal and 2 health pots.
Core- Rod of Ages, Sorcerers Boots, Rabadon's Deathcap.
Everything else is according to the enemy team but these are the optional reccomended items:
Void Staff, Abyssal Scepter (magic resist and magic pen that you'll be able to use because your spells are close ranged compared to most), Morello's Evil Tomb( cooldown reduction and mana regen), Archangels Staff (lots of mana, AP, and mana regen, Rylai's Crystal Scepter(durabliity and slow), Banshee's Veil (great for anti-cc), and Zhonya's Hourglass (great defense and lots of AP).

Farming and playing with Annie:
Hit a minion with your auto attack a few times, then use your Q because your Q refunds all of your mana if it kills a minion (I start with this at level 1 because of that reason). You level up your W as quick as you can because it does the most damage and is a cone-based attack. Get E at level 4 to help add to your defense. R is your ultimate attack. You don't want to waste your R on a single target if you can help it. Sometimes if you find a character alone, it's alright to use it in order to nuke someone. You are Annie, you are feared in mid for a reason.

Early game:
As Annie, you're not going to be much of a threat early game. 1 spell is not enough to take on anyone, even if you have your stun up, especially starting out with a sapphire crystal). So all you really want to do is farm up to level 6. You can harass a little bit, but don't harass too much because you don't have a great amount of mana regen. If you are good at mana management, you do not need mana regen period. Make sure to farm with your Q. Don't be afraid to waste your stuns (if you know you can't kill your opponent) on minions. Annie requires a bit of gold. You want to get your Rod of Ages as fast as you can (even before your boots!!!)

Mid Game:
This is where you become dangerous. You are pretty well farmed and you have Tibers . You're able to gank with your stuns and deal a lot of damage. By now, you should be able to have your Rod of Ages up and begin to work on your boots. Annie's durablity and damage at this point make you especially great at ganking. Make sure to work with your team with the stuns and focus down targets (whether you get the kills or not because it's a team game.) After your boots, you should get your Rabadon's Deathcap. You are going to be a nuking machine after this item.

Late Game:
At this point, people are going to be crying as they see you skippnig down mid. This is where your item build begins to vary depending on the team composition they have. Normally, if you're a good Annie, you wont be making it to late game, but if you have, congratulate your enemy. By now, you should be able to 2-3 hit nuke anyone, especially if you have ignite. Just make sure to work as a team and use your AOE stuns. This will almost guarantee you victory.