Hy! I am not pro and thats my first build. I wanna teach u just basics of anivia.
p.s. my English is not very good.

PROS

Op damage

AOE damage

OP passive

CONS

Hard to land q

Hard to farm early game

Need too much mana

Has only one egg :D

1 Remember u cant just go towards enemy and land your flash frost. It is almost inposible because its very easy to dodge it. If u wanna land your flash frost u need to get close to the target and the best way to do it is flash or ultimate.

2 Crystallyze can be used in manyways.I use it to block the way to jungles, it is also good escape tool. In team fights you can use crystallize by spliting enemy team.

3 Lots of players who plays anivia first time dont now that frostbite deals double damage if the target is slowed or stuned by anivias abilities.
The best harassment is r+e or e+r(if u do your flashfrost and ultimate fast it still deals double damage)

4 Her ultimate can be used to deal double damage from her frostbite,to slow and catch enemies, to slow enemies so they can't dodge your flash frost or escaping. It also can be used by farming large minion waves. In teamfights it is very effective because it deals aoe damage and slows carrys attack speed.

5 If your level 9 your frostbite cooldown is low so you can do your ultimate to slow enemy, land frostbite, flashfrost and because of low cooldowns frostbite again.