Annie is a squishy champion but is one of the best nuker in the game. If you get 3-5 kills in the game before dying you will get OP at about lvl 8. If you dont get fed in the beginning ,dont worry. Your dmg at lvl 16-18 will be much higer than your enemies!

When you get into a fight first place Tibbers (if his not on cooldown) on your target and quickly after press "w" and for the final dmg press "Q".

When your in a 3v3 allways use Flash and Clarity. Many good and bad players use Ignite but its not necessary. With Annie they wont get away with little hp , they will be dead!

In 5v5 use Flash and Clarity/Teleport.
Lvl 1-7 you will probably get oom so Clairty is a good option but you will not be needing Clarity later on so that why i usually use Teleport.
Early in the game Annie will get oom and probably get really low on health so although you could use Clarity it wont help with your HP and later on Teleport will help your team alot more than Clarity. Early in the game Teleport is also very important if your not using Clarity so you can recall and teleport back with full HP and mana.

If your not over lvl 12 , use Ghost insted of Flash.

You want to mainly focusing on getting much ability power, feel free to take any item with much ability power.

Lvl 1-6:
Pros :
Nice Dmg
Cons:
Out of mana and helth quickly

Lvl 7-14
Pros:
Higher dmg than most champions.
You wont get oom easyly
With tibbers you can nuke a squishy enemy in 1-3 sec (depends on if your fed or not)
Cons:Still squishy and enemy team will probably try to kill you first in a team fight.

Lvl 15-18
Pros:
If fed you can take on 2 enemies and nuke them before you die, maybe even 3 if they are low HP from the start and you got Tibbers. Still sick dmg.
Cons: Same cons as Lvl 7-14

Im sorry for horrible spelling and gramma. Im from Europe.