
Shove your lane under her tower to punish her inability to effectively farm under turret. She relies on freezing her wave to succeed in her early laning phase against aggressive opponents. Crash your wave to turret and reset the wave to force her from safety. Forcing her to expend her mana to keep her wave frozen is the best key to your safety alongside warding to avoid her jungler merc'ing you, she'll have no mana to harass you.
Do NOT overcommit when she egg. If you aren't sure you can kill her while she's reincarnating, pop her egg and back off. Wait for CD's and kill her when her egg is down. She will have no choice but to play safely and temper her aggression with her fear of dying in the event she misses her skill shots. She is weak to well coordinated dives and flanks.
She is skillshot reliant, avoiding her Q is important in her early levels. Be aware of your autopathing when she walls you - anivia is reliant on you making the wrong choice and walking into her abilities. Do not stray too close to her turret or terrain, a good anivia player can and will wall you to force you to take turret shots or pin you between her wall+terrain for you to eat her full combo and likely die.
Her midgame is strong because she is a seige and pick goddess. Ward well to avoid getting caught by unfavorable exchanges in the jungle where the tight quarters make her an undeniable force. She can wave clear extremely well to avoid sieges until late game, so rotate to a lane where she isn't to push down a turret. If you have a champion that can feasibly build it,
seriously screws her. She is one of the slowest moving champions in the league and you can simply out rotate her that way, even better if you can assassinate her while she's rotating to respond to a push. If you have a competent assassin she is a decent target - you can kill her and force objectives where her absence is most felt - particularly drag and baron/herald where her zoning tools in the river can spell death for your team.
Late game she plateaus and becomes more of a utility bot with her zoning tools. Her burst damage will cap out and become less effective as players get more gold to buy defenses over the course of the game and can simply withstand her burst. That said, I would not underestimate an anivia that invests into a
purchase to specifically melt tanks and super minions, allowing her to scale along with your team's defenses in a way long after her AP core is finished.