Farm with AA and last hit with Disintegrate because then you get your mana back and also half the cool down rate.

Poke when your Pyromania is ready - first hit with Disintegrate, then with Incinerate and then with your AA. Your opponent will be stunned for the whole duration and not be able to deal any damage towards you.

Be careful with Incinerate because of its long cooldown it leaves you vulnerable (especially when you get ganked).

Use Pyromania to zone your enemies away. If an opponent sees that your Pyromania is ready he will likely stay away from you. You can zone your lane opponent away from minions or it can ward off junglers. Be careful because the enemy jungler could wait until you used your Pyromania so better back off and engage again when you have two parts of your stun back. When you get ganked use Pyromania on the nearest opponent as soon as possible so you can get another stun as soon as possible afterwards. Especially, if you get tower dived during a gank try to stun your attacker to get a kill instead.

Annies wave clear is not very good but you can make things a little bit easier on range minions with AA followd by Disintegrate.

Use Incinerate and/or Molten Shield to get two points into your Pyromania. This is mainly the case when you are leaving the fountain after you died or recalled.

Try to stun multiple enemies with Incinerate or Summon: Tibbers, especially in a team fight. You can use Summon: Tibbers to initiate (in combination with Flash) or to end a fight.

Always keep track of your Pyromania so you always know if it is ready or to make it ready when you need it!

Always stay with your teammates!

Annie has a lot of burst so you can take out squishy champions very quickly. If a superfed enemy carry cannot be caught by your teammates you can Flash on him and kill him with Summon: Tibbers (or at least zone him out of the fight).

If you already have three Points in your Pyromania you can use Molten Shield to make it ready before you use Summon: Tibbers. This is a nice little trick to surprise people but it does not really work against more experienced players.

Remember that you can also zone with Summon: Tibbers, e. g. when taking drake or baron - your opponentes will first have to deal with him before they can deal with you.