This is my first ever build guide (any tips are appreciated)... I've played Anivia close to 1000+ games and this build is what I have found to be most powerful for a Solo Queue Anivia player. This guide aims for super high creepscore and an extremely strong teamfighting Anivia.

This rune set up is made for having extremely high burst damage throughout the game (especially when you finish your deathcap). If you are having mana problems you may want to consider picking up MP5 Glyphs, However I have never found mana to be a problem on Anivia with Tear of the Goddess + Blue buff.

Like the Rune page, these masteries are set up for max burst damage throughout the game... By going 21/0/9 I can get all the bonus damage needed/wanted along with the buff duration talent which is huge on Anivia considering how strong she is with Blue buff.

These items are setup to acheieve a smooth transition from early to mid game with and extremely amazing late game finish. By building Tear of Goddess and RoA first, we are starting the game with items that stack over time and only give us max effects and power late game. This is fine considering Anivia is a farming champion who naturally scales to huge bursts late game regardless of your starting K/D. However, try to keep the deaths to a minimum considering it will take away from your CS. When we reach Deathcap, this is the time to start being agressive. Your ability power will hop from around 100+ to over 400+ by just finishing this item. This is due to the runes and masteries we have selected. This is when you want to stop being passive and start bursting people down with a couple quick combos. Void staff will only help your burst and you might want to consider picking it up before finishing ArchAngels depending on the other teams MR.

This Skill Sequence is aimed at making Anivia the hardest nuker she can possibly be. E does massive amounts of damage when the enemy is frozen, and therefore we want to max out our E (the big guns) as early as we can. Q also does a decent amount of damage, but early game we are just using it for the frost affect, so take this and max it up after your E. Unless you're getting ganked constantly without wards, W is a skill you can hold of on getting untill late game. I like taking it at lvl 8 so I can have an extra fallback spell if I make a mistake, but if you're confident you aren't going to make a mistake or get ganked, you can take this around lvl 12 or 13 if wanted. Max your R whenever possible, like most ults, does massive amounts of damage if used properly.

I personally love taking flash and teleport as my summoner spells. Flash is simply gorgeous on Anivia, you can do so many things to use it to your advantage. Example: Mid is low and only 1 RE combo away from death. Act passive, wait for them to get somewhat close, then just flash at them and use RE. I cannot tell you how many times i've gotten kills mid because of flash. Flash is also an amazing escape spell, not only can you flash over wall in game, but as Anivia you can even MAKE YOUR OWN!!! Lets say you overextended mid and are getting ganked cause your ward just wore out. You can try to land a Q and use your ult to slow them down, But some situations you just can't get out of. Having flash on Anivia gives you the ability to place a wall in front of you and instantly flash passed it, giving you a HUGE seperation from the other team. This can even be used in team fights or when getting caught out in the jungle.
I take teleport simply because I do not play aggresive Early game and therefore Ignite would be useless for me. Clarity is ok, but doesn't scale well on Anivia and is kind of useless compared to teleport. Teleport is amazing because it gives you the ability to hop across the map and clear huge waves instantly with your R. It also gives you the advantage mid to Recall back to base (get full life and mana) then teleport right back when needed. Feel free to use other summoner spells on Anivia depending on your play style, but I just find this combo to be the most effective for the way I play.

Pros:

Amazing Farmer
Amazing CC
Amazing Burst
Free Guardian Angels

Cons:

Need Quick Reactions to CC properly in teamfights
Somewhat slow and squishy
Can be countered easily by silence (Talon is a B***H!)
Needs Blue buff or will run out of mana pretty quickly

When you have Blue buff on Anivia, you should check with your jungler and make sure its cool if you steal wraithes and wolves whenever he is off ganking. This helps your team in 2 ways. 1) you're getting an exp & CS advantage over the mid player you're laning against. 2) Since the new Jungle, the creeps will spawn in time for your jungler when he is back from ganking and he will also recieve more gold when he kills them... Win Win

While teamwork is amazing to have, a Great Anivia is like a puppetmaster in teamfights. Use W to keep specific enemies from your Carries, use Q to stun their Carries, and use RE to burst your teams targets. People like Tryndamere will be easy for Anivia to shut down in teamfights if played properly, RE combo him down to like half life... Then stun him with your QE combo, when he pops endless just seperate him with W till he's ready to die. Then just burst him down with whatever you have. If you do simple things like that to the other teams "fed" champs, your team should have a huge advantage in teamfights!

Anivia's most Unique Skill is probably her passive. Think of this as an opportunity for your team to deal "free damage". If you get egged in a teamfight, the other team has 2 choices: kill you and give your team a free window to pump out DPS. Or: turn their attention to your team and let you clean them up in 6 seconds. Either way, this passive gives your team a huge advantage when grouped together in teamfights. Definentally keep this is mind throughout the game as well. Play a bit more aggressive when egg for is ready, and play super passive when it's not. If you can do that, You can easily keep your deaths below 2/3 everygame you play as Anivia.

Farming is pretty basic on Anivia... Get Blue Buff, drop your ult, get easy creeps. Just remember to ward your lane so you can push to their tower to clear a wave without worrying about a Jungler gank

Anivia is a farming champ. Early-Mid game usually consists of farming, getting blue, farming, warding, farming more, getting another blue, then farming some more. This build is set up to give you enough life/mana to survive early and mid game and just farm without missing a creep. If you are a super aggressive player this build might not be right for you. Aim for 200-300 CS before team fights begin and you will be bursting Tryndamere down before he can say Endless Rage..... Seriously.....