Sometimes it is smarter to approach an enemy with 3 Pyromania charges instead of 4 to appear vulnerable. You can then quickly charge the stun with Molten Shield. It can also allow you to break Banshee's Veil with a weaker spell before using a spell (especially Summon Tibbers) that stuns them.
This can also be an effective strategy to lull enemies into a false sense of security.
During the laning phase, try to find a good balance between storing your stun for use and continuing to use your spells to maintain a strong farming game.
Don't rely on Molten Shield to keep you alive. Its damage isn't great for countering AD carries with life steal, and early game its defensive properties are minimal at best. It is mainly used to charge up a combo.
WhileIncinerate can take down groups of low health minions early game, positioning the cone so that it also routinely damages the enemy champion can be very useful. Dropping their health like this can be followed up with a big Summon Tibbers/Pyromania burst for the kill.
Annie'sSummon Tibbers can be controlled, like most pet units, by holding Alt or activating the ability again before moving.
During the laning phase, use Disintegrate to last hit minions since it refunds its mana cost when it kills a unit. Use this to quickly stack Pyromania.
Rod of Ages is a strong item on Annie as it allows her to be very tough without sacrificing too much ability power and Catalyst the Protector's passive lets her to stay in the lane early game. The increased health pool is also useful as she needs to get in close to the enemy to cast all her spells.
Abyssal Scepter is a good option for Annie when the enemy team has lots of magic damage. It provides magic resistance, but still contributes to her burst potential with AP and a magic resistance reduction aura.
All of Annie's spells deal magic damage, therefore any form of magic resistance will mitigate her damage significantly.
Banshee's Veil offers a spell shield to negate 1 spell from Annie. Its magic resistance and health will help tremendously in surviving Annie's burst, while also usually blocking Annie's opener, which is typically a stun.
Quicksilver Sash is a cheaper alternative, and allows you to block her stun specifically, instead of just one ability.
Do not underestimate the damaging aura from Annie'sSummon Tibbers. The longer the fight lasts, the more damage you will take from it.
Do not disregard Tibbers completely, however. Its attack damage and damaging aura can easily put a tense fight against Annie in her favor if left to attack you.
Alternatively, use ranged attacks and abilities to kill Tibbers while keeping out of range of Annie's spells, the advantage to this being that Tibbers will most likely be easier to kill.
Tibbers is considered a minion therefore Smite and champion abilities that work on minions and monsters only (such as Syndra'sForce of Will), will work on him as well.
Be alert for the visual effect that appears when the stun from Pyromania is ready.
Because Disintegrate refunds mana when used to last hit minions, be cautious around an Annie using autoattacks on minions. She is likely to have 3 stacks on Pyromania and is waiting for someone to engage her. She will cast Molten Shield, allowing her to stun on her next spell.
Molten Shield acts like a Thornmail. Be careful when engaging her if you are using a champion that relies on auto-attack.