Annie is currently one of the best nukes in league, especially early game if you learn to rush items. This build is pretty much an offtank annie with spell vamp.

PROS:
Stun
Aoe
Nuker
great 1v1 champ

CONS:
squishy early game
slow
usually the target especially if fed

First start off with Doran's Ring, you don't need pots. Learn to play passively and LAST HIT with Q. Also harrass with q every once in a while if you want a kill later on.. don't lose a lot of health you don't have pots unless if you recall to buy.

Second you need to rush needlessly large rod. this is very important to nuking early game.. once you get the needlessly large rod you can run around and gank, you WILL hit very hard and you'll be able to combo people very easily.

Third you need your sorcerer's boots. gives you 2 speed and 20 magic pen.

After boots get your Blasting wand then once you get enough money for rabadon's deathcap, buy that as fast as possible. Now you'll really be able to nuke some s#*t up.

After deathcap, start to buy items and build into rod of ages once you get this farm some extra minions and get your 20+ ability power and your extra health and mana. Rod's is important because you need the AP, definately the mana, and the health is very required for surviving.

Next get the Rylai's crystal scepter, you get 500 health, and instantly 80 ap. Also you can slow people with it.

Will of the ancients gives you 25% spell vamp and 50 ap, 30 for your nearby allies. Including you. so you get 80 ap total. Very useful for surviving in teamfights and getting a good amount of ap.

If your enemy team is very tanking and has a lot of magic res, void staff is the best choice, 70 ap but it has 40% magic pen.

Annie's passive Pyromania: After casting 5 spells, annie's next spell will stun the target for 1.75 seconds.

Q - Disintegrate: Each time you kill a target, such as a minion, you get refunded mana
W - Incinerate: AOE Fire, best using this for stuns, you can stun a whole team.
E - Shield reducing damage from basic attack, returns damage back
R - Summons tibbers, dealing damage when casted, tibbers deals damage to people in his area, he auto attacks 70 damage. control tibbers with ALT and right click

Use Q when farming. First auto attack, then when the minion is low enough, use q to kill it, you will get refunded mana.

Use w to kill crowds of minions and to nuke multiple people. it is best to use this skill in a teamfight to stun.

before you enter a teamfight hit e, whenever people regular attack you, it returns damage.

R can really do a lot of damage when you cast it to people in the area, tibbers pretty much has a sunfire cape so he does damage to people around him. he hits 70 damage. control tibbers with alt and right click.

In a ranked game it is best to play annie in mid, you will dominate the lane and nuke anybody if you time it right and harrass just the right amount before you kill them. In ranked, ROD's and RYLAI's are required for survivability. It gives you the health for defence. Make sure to buy lots of wards every time you go b or respawn, a ward is only 2 minions. Also annie farms easily so it shouldn't be much gold. Early game make sure to take advantage of your nuking abilities, and as soon as you get your needlessly large rod, get to business and gank. make sure to have your stun up before you kill. In teamfights use w to stun their whole team. Before you enter a teamfight hit e, then stun, after that drop tibbers and use q. Annie does a lot of AOE damage, make sure to take advantage of it. Especially in ranked, you can output loads of damage. You can get gaurdians if you really need to as your last item if you're more concerned about surviving.

Use your w skill to stun, make sure you have it up if you are gonna help gank. YOU ARE THE NUKER OF THE TEAM, make sure to be in all of your teamfights.

Auto attack then Q to kill minions you get refunded mana