"Do You Want to Play Too?"
After Annie casts 5 spells, her next ability will stun the enemy target(s) for 1.75 seconds.
Annie's passive ability is the reason that she is so good. Her consistently reliable stun is amazing for initiating on single and multiple targets. Everyone fears the Annie with the swirling cloud around her because they just know they are going to get stunned. Use your Q to farm and then stun the nearest enemy and follow up with the rest of your skills to harrass and burst down opponents when you have your ultimate (Tibbers).
Annie flings a fireball at a single target dealing 90-250 magic damage (+ 0.75 per ability power, AP). If it kills the target, Disintigrate's mana cost is refunded.
This is the skill you will use most to farm up last hits without using mana. Early in the game, don't use this to harass as you will soon run out mana.
Annie casts a cone of fire in front of her, dealing magic damage to all enemies in the area.
This is the skill that you will want to level up first as it deals more damage than your Q. The AOE is also good for stunning multiple enemies if they group up. Again, early on, don't use this ability to farm as it will just drain your mana and you won't be able to get a kill at level 6.
Molten Shield (E)
Places a shield around Annie for 15 seconds that increases her armor and magic resistance. Additionally, enemies will be dealt magic damage whenever they attack her while the shield is active.
Annie is so squishy that this shield rarely mitigates any damage. It does provide a decent armor and magic resistance buff, but It's only good at returning a portion auto attacks. Use it to cycle your stun faster after opening up with your R, Q, E combination.
Ultimate: Summon:Tibbers (R)
Annie releases her bear Tibbers, dealing magic damage (200-450 magic damage +0.75 AP) to enemy units in the summoned area. For 45 seconds, Tibbers can move and attack at Annie's will, while continually dealing magic damage to surrounding enemies.
Tibbers is great at opening with your stun as it has a decently large area of effect (AOE) to stun enemies at a distance. You can then follow up with the rest of your skills (see below for combo). Besides the damage, you can use Tibbers to zone your enemies in lane, deal AOE damage in a team fight, or push down towers. Use Alt + click to control Tibbers.
Put one point into Q and level up your W, taking your R at levels 6, 11, and 16. Level up E last to maximize your damage out put with W and then Q, respectively.
Combination: R, Q, W, Ignite, E. Repeat if necessary.
Once you have a stun ready, open with Tibbers (R), then follow up with all your damaging spells. Since the target is stunned, you should have plenty of time and be in range to land them all. Follow up with ignite to secure the kill. This should get most champions really low at levels 6-7, if not kill them outright. You can also use flash to get into range and surprise them with your stun.