Not Updated For Current Season
After seeing so many players fail at Anivia; I finally decided to make my own guide for her. She's my main champion and basically this is the best survivabilty - ability power build.
[*] Flash - Saves you from ganks and is also a terrific chasing skill
[*] Ignite - Pretty much the best caster skill out there. It will burn down your enemies, especially health regeneration relying ones.
[*] Greater Quintessence of Fortitude - Makes your Anivia very hard to kill early game, so you can afford playing agressively as much as you want.
[*] Greater Glyph of Force - Insures that you will constantly be gaining Ability power, and makes up for all the survivability items you're buying at start.
[*] Greater Seal of Clarity - The bad thing about Anivia is that she can run out of mana quite fast, that's why we get mana regeneration per level runes. Also you should be aware that it alone won't be enough. When you can try to grab a blue buff.
[*] Greater Mark of Insight - Magic Penentration; Best option.
[*] Start off with a Ruby Crystal. This will gain you a huge advantage early mid game.
[*] Follow it with a Catalyst of Protector. Since you don't have Clarity or any other mana items. You should have this item at level 6. It will allow you very fast farming and a decent health - mana recovering. After you get this item you should get at least 4 levels before returning to base.
[*] Mercury's Threads - There ain't better boots to choose from. They will grant you major survivability. You can consider getting the Cool down reduction boots; But in my opinion they're not worth it.
[*] Mejai's Soulstealer - By the time you get it you should already have a few kills; If you aren't getting any kills and are having a hard time, leave this item, and replace it later in game with Deathfire Cap.
[*] Rod of Ages - Very decent item, is a must on every Anivia
[*] Rylai's Crystal Scepter - Health + ability power - They will have a harder time killing you than a tank.
[*] Abysall Scepter - If their team is heavy ability power grab it.
[*] Frozen Heart - If their team is heavy damage per second grab it.
[*] Zhonya's Hourglass - I basically buy this item for it's active. The stasis can save you so many times :)
Anivia is probably the best farmer out there; Ulti the minions and after that send a flash frost to collect the gold. This will save up on your mana more than if you would just use your ulitmate for minion kills.
[*] Flash Frost - Q Skill - After pressing the Q again you make the flash frost stop and stunning where you hit the Q
[*] Rebirth - Do not relay on your rebirth skill too often, try to play as if you didn't have it. Because thinking you're immortal will only get you dead.
[*] Use Crystallize when running from someone; Or chasing someone. Also it's a very nice skill to combine with your ultimate. You can trap your enemies (making them walk in your ultimate for a longer time --> Weakening them, killing them. You can also use the skill to check out bushes.
[*] Combination of Flash + Ignite is a deadly finishing off move.
Well I hoped you liked my Anivia guide. It's pretty much victory after victory. Please try it out before you rate it :)