Not Updated For Current Season
Since yet I already played a lot of Games with Anivia, who I think is one of the hardest, but most funiest Champions to play. She can be usefull, for quite every Teamsetup, since she is a great Supporter, with giant Burst-Dmg and a awesome farming.
This is, what i would call, the hardest phase, since Anivia has a very slow last-hit animation, and a weak auto-hit, you have to be very in the game, when you want to get creepkills. The first Spell I choose is useually Flash Frost, which can be usefull for last-hitting creeps early on. When playing Anivia, you should try to get on a Solo-Lane, have no worries to go for a 1vs2, you have a long Range, with your auto-hit and a even further with your Spells. Anivia is very gold intensive, so you should do your best at Farming. When you reach LvL 2 you can start some Harassing, use Flash-Frost try to get the double hit and after that throw your Frostbite, which is a very explosive Burst attack, when your Opponent is slowed. If you are on the Midlane, and your Opponent is Low, try to Flash into the right Position, Flash-Frost, Frost Bite and Ignite him.
When reaching LvL 6, you can easy Combo down Creep Waves, use your Ulimate on them, throw a flash Frost and most of the creeps die imidiantly, if there are Cannon-Creeps, you can Frostbite them, to get the kill on them, too.
You do tons of Damage, so you have like no surviveability. When you play Anivia it´s awesome, to have a Ingaging-Tank, like Malphite, Rammus, Amumu or Galio in your Team.
You have to stand behind your Team and try to Place your Ultimate as good as possible and get it on as long as possible. Throw your Flash-Frost and try to hit as many Opponents as possible, before you Frostbite the Squishy Carry´s of the opposite Team. Since such Combo´s are very Mana-intensive, getting the Blue-buff is very important for an Anivia.
What to do if I get ganked?
If you get ganked, try first to place your Crystalize infront of Enemy Champions trying to Chase you.(You can also place Crystalize into the bushes,to check if somebody is in it)
Try everything to get to your Tower, because when you get your Egg, most Enemy Champions won´t try to kill you with Full-life in Tower Range.