Ive done this build for a long time and it seems to work out great for me. I go for dorans first just for 100 health and the AP which should do pretty good damage at the start. Then i grab sorcerers shoes and rylais as quickly as i can possible. After i go for void staff for the magic penetration and if i dont have enough i just sell my dorans for a bit more money. Then comes rabadons which will give alot of AP followed by Zhonyas hourglass. Finally i would get abyssal scepter for more AP and magic resist incase the other team has alot of AP.

3 Greater Quintessence of Potency
9 Greater Glyph of Potency
9 Greater Seal of Intellect
9 Greater Mark of Insight

I used my quintessences and glyphs for AP. Since i have enough AP i use my seals for mana and my marks for magic penetration.

For my masteries i went 9/0/21. For offense i used 9 skill points because its helps with your AP, cool down reduction, and magic penetration. Then for defense i didnt use any skill points because Annie is not a tank person... she is a caster so i put 21 skill points for utility. Utility is important for casters because it helps with many things such as maximum mana capacity, mana regeneration, cool down reduction, Exp gain, base movement speed, and more.

The items in this build are sorcerers boots, rylais, void staff, rabadons deathcap, Zhonyas hourglass, and abyssal scepter. These items give alot of AP and also to stay alive longer, the items give you magic resist and armor. The items in this build should be very helpful if u play annie right... hope it work out for you.

In skill sequence i try to max out incinerate first because it hits more than 1 enemy at a time if you land it correctly. Then I max out disintegrate in case an enemy attempts to escape, you can use the skill to kill them before they are gone. I pick skills in this order to do as much damage i can early and late game. Next i get my ult maxed out before molten shield. I also always stun with Tibbers for the AOE stun. Once the AOE stun is landed perfectly... your team can help mow down the enemy champions that are stunned and go for others later.

For summoner spells I picked Flash and ignite. (Flash) I use for enemy champions running away or if I get into trouble i can flash away before they kill me. (Ignite) I use in case an enemy champion is low on HP then I can pop ignite and they have a great chance of dieing unless they are healed.

I made this build to see if i can help anyone in the world of league that needs help with playing Annie. Summoners who play and use this build I hope it will be a good build for you guys. Have fun playing league everyone and I really wish you guys spread this Annie build =D.