Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
Start with mana then get mobies then get catalyst then get mejais and then hex then zhonyas and then Nashors if you haven't won by now.
I take Clarity and Ignite for obvious reasons. You might want something else instead of Ignite but that's totally up to you. I specced for it because I prefer when my nukes hit like America.
I like to jungle because my wall can seperate team ganks and make team jungle 5v5s turn into team jungle 5v2s with one well placed wall.
The rest is pretty straight forward, I'm not going to tell you how to play because I'm prolly wrong. Everyone else plays anivia better than I do anyway so I'm not even going to bother being wrong on the internet like that. These are the items and spec I prefer when I play Anivia and I hope this helps you realize that this is one of the better ways to build her. Also I like getting Frozen Mallet on rare occasions for giggles and extra slowing so my team can gank without any problems, and so I can nuke like crazy without them running away from me, or trying to 5v1 me and still fail.