Annie is an overall easy champion to learn! It is easy to farm due to your Q refunding mana on minion kills. You have a built in stun to help with team fighting and an easy lane phase. She deals plentiful damage after you get your early game items. She snowballs really hard after 2nd blood.

Early game first blood is fairly easy. You want to make sure you're in the lane first before your opponent. Once you are in lane get your first three Q's (Disintegrate) on minions. Once you have your three charges kill off the rest of the creeps with your auto attacks. Since you were in lane first you will level up to level two faster. As soon as you are level two, Quickly unlock your W then Q/W your lane opponent. your lane opponent should be already fairly low and stunned. While your lane opponent is stunned, use your ignite and auto attack as much as you can and finish off your enemy with the Q's.

You want to toy with your lane opponent. Everybody knows Annie has a stun passive built into her kit. But you never want to have it up. Having it up makes your enemies cower in fear under turret which is a no no. You always want to have only 3 charges up unless you are farming with Q. When you only have 3 Charges on the stun, they won't know when you'll let it out. You want to surprise them by Using the E ability quickly and following up with Tibbers Bear stun. Never use the bear unless you have a stun. You deal the most damage because the enemy will be stunned with an AOE (Area Of Effect) damage from Tibbers

As Annie, you always want to lock down the carries first. Initiate with the Bear stun. When you initiate with the bear stun you deal the AOE damage as said in the previous paragraph and it can also stun multiple champions at once. Once you have locked down the Enemies your team should follow up and you can just spam all your abilities on the carries.

Pros
Annie has a built in stun
Annie can snowball after first blood
Annie has high range


Cons
Annie has very slow movement speed even with Boots
Annie has no escapes other than flash
Annie is useless when she does not have stun.