Anivia is a bursty mage that can also deal some consistent aoe damage with her ult. She can by one of the best mids in lol if played correctly. I choose to build tons of mana and ap early, and build health for some tanking ability late game. Building health late also helps her egg, which is arguable the best passive in the league, if used correctly.

I choose to give Anivia pure AP runes. Magic Pen marks and quients, and straight AP gylphs and seals (ap per level). But i have used cd and mana regen runes that work well too.

For masteries I go 9/0/21. And i go less AP and more utility for masteries. I like having the extra gold and health regen.

I think Anivia is best going for tons of mana early, because her base damage spells are high for low levels and her egg makes her rather tanky and can be used to scare enemies from tring to pressure you to much. Since Anivia is also very mana hungry, not only early game but late game aswell, having tons of mana allows you to stay in lane a little longer. Then mid game I build into ROA and Archangles, and then add a deathcap. This gives me alot of AP, which allows me to burst down squishy champs. Late game I build a warmmongs and crystal scepter. I do this to get tanky and stay in battle with her ult, which is short on range, alot longer. All this health also helps her passive, giving her more health to survive her egg.

Anivia may be one of the best mages in team fights. Her ult allows her to deal damage and slow their whole team, her q is good to stun carries that sit behind their tanks, her e allows her to deal a good burst of damage and has a short cd, and finally her wall can be used many different ways. I like to use her wall early in team fights to pick one target and keep the rest of their team off your team will you burst him down. Her wall can also be used to gank and prevent escapes, or block off the enemies when getting ganked, and also can be used to block the enemy from you or a teammate when running away.

It's easy really, just one word: ULT.