My goal at this very moment is to get as good as I can with every league of legends champion or at least a very large number of them. Some people say the best defense is a good offense, this game isn't only about playing your champion, your play style, luck, connection, teamwork/teammates, your enemy, and how well you know their champ(very important) all make a big difference. Just remember to "Think and Predict the Future" you can quota me on that.

I was playing dominoin the other day; and my team was almost all AD, with no AP champs. Well I had 3 choices at the time Annie, Katarina, and Kassadin. I was like Ive never played Annie in dominion. So to save my team from Thornmail I had to give the enemy team 2 choices deal with the other 4 or me. I ended that game with 15/1/7 in 11 minutes. I was 13/0/2 with only boots(I never returned) when I finally died. That was the first time I played Annie in 9 months-ish and was my first dominion game with her. The moral of the story work with what you got and try to form a synergy with your team and destroy the enemies will to continue.

Items are somewhat flexible but generally you want to keep the idea the same its just the execution that really changes. If you have the gold of a part to an item get the part its better than nothing; if you returned or died that is. REMEMBER there are optional item trees.

Sorcerer's Shoes Is your start item. It gives you magic pen which is always good and also the speed to get to mid then top or straight to top fast with ghost. Going mid then ghosting top is the best plan you team should still be alive and there's too, but they should be hurt pretty bad giving you some easy kills.

Rabadon's Deathcap Annie's number one best item for killing, huge because of both the 140ap and the passive +30% ap. I call this the red mage hat, I love the red mage!

Void Staff 70ap and +40% magic pen(with the red mage hat you get 91ap and the runs plus boots plus void staff gives you 39.95 magic pen)

The next 3 very...

Will of the Ancients 80ap(104ap with red mage hat) and 25% spellvamp(the aura is nice but its team effect boost is only moderate.

Morello's Evil Tome 75ap(97.5ap with the red mage hat) 12 mana per 5 secs and 20% cooldown reduction.

Abyssal Mask 70ap(91ap with the hat) 57 magic resist and the Passive which stacks nicely with magic pen -20 magic resist to all enemies around you.

Others you may want to look at are:
Zhonya's Hourglass ap armor and survivability
Rod of Ages ap hp mp
Rylai's Crystal Scepter ap hp slow
Banshee's Veil hp mp survivability
Deathfire Grasp ap mp per 5 and a pretty strong 1 min activated CD
Archangel's Staff ap mp and 3% of mp to ap
Mejai's Soulstealer ap /CD snowball item if your going to die ever not worth it
Lich Bane ap plus every time you use an ability the next auto-attack will hit harder
2 sec cooldown

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Its not Dominion but its a good example of how to play Annie (this is not my video)
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This is not my video but I think this is a good video
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Just a great video