This is my Anivia build with both my old build (build one) and my newer build (build two). I find both to be worthy of Anivia so whichever you choose is by preference. They are similar but have some uniqueness to them as well. In later chapters i will explain my reasoning for both builds and alternatives. Anivia has always been my all time favorite champion and my friends suggested i post my build and see what others think, so here it is.
Okay first we will start with runes, the runes for both builds are the same. Greater Mark's of Insightx9, Greater Seal's of Clarityx9, Greater Glyph's of Forcex9 and Greater Quintessence's of Potencyx3. I use the Greater Mark's of Insight for the magic penetration, this is the standard mark for most ap champions. Greater Seal's of Clarity, i find these seals to be better than Greater Seal's of Replenishment because Anivia has CRAZY mana problems all throughout the game whereas the Replenishment seals are for champions who are not as mana hungry at late game, even with these seals, the masteries and the items i find her to be very mana hungry (this could just be that i like to spam). For glyphs i like Greater Glyph's of Force for the extra ability power later in the game when enemies start to get tankier it will offer more damage however, the Greater Glyph's of Potency is also very nice on Anivia in case you want to have a bit more ability power earlier on. Now the Quintessences are totally up to you, for a long time i used Greater Quintessence's of Swiftness when i first started learning Anivia because she is one of the slowest champions in the game and she can be very hard to learn but having a bit more movement speed can help a new Anivia player a lot. Now that i am more experienced with her i do use the Greater Quintessence's of Potency for that added ability power, note that both Quintessences are acceptable and you can go either way and still be okay.
Okay now for the more detailed chapter.
To start you can go two ways, Sapphire Crystal and 2 Health Potion's, or Boots of Speed and 3 Health Potion's. I find my self starting with the boots rather than the mana because that extra bit of speed is great on Anivia and the mana early is meh.
Okay for the first back item i have two different items, the first build i have a Tear of the Goddess which is later built into Archangel's Staff which offer great mana regeneration, mana pool, and ability power, or you can buy Chalice of Harmony which will be built into Athene's Unholy Grail which offers mana regeneration per mana missing, ability power, and cooldown reduction and magic resistance which can be good against a hard ap lane.
Next you should work towards a Rod of Ages, this one is pretty standard for squishy champions like Anivia. It offers health, health per minute, mana, mana per minute, ability power, and ability power per minute not to mention that every time you level you get an amazing regeneration buff.
After Rod of Ages you will want to get your Sorcerer's Shoes for the increased speed and magic penetration.
Next up is the famous Rabadon's Deathcap for the crazy increase on ability power!
After the DCAP, as i call it, it is time to finish that first half-item you bought, if you went Tear of the Goddess i find that at this point you should have quite a bit of stacks (again this might be due to my love of spamming), but if you want to wait a while longer then that is okay too.
Next up we have Zhonya's Hourglass a pretty much must have on Anivia for some awesome armor, ability power and invincible buff.
Now for our last item i used to have Abyssal Scepter for some extra magic resistance but since it was nerfed i switched to Void Staff for the magic penetration.
As a side item, if you find yourself needed some defense try getting a Guardian Angel, for some magic resistance, armor and a rebirth, that's right Anivia double rebirth FTW!
For skills i start with Flash Frost for some slow and stun and when you get Frostbite first it does not do a whole lot of damage especially if they are not slowed, so Flash Frost and then Frostbite. I get Crystallize at 4 and leave it for the last few levels, i do this because it is really just a support spell. It can be used offensively and defensively, walling off enemies who are chasing helps a lot, Anivia is a great runner both with slows, stuns, Rebirth, and walls. It can also be used to wall off enemy escapes but another way i use it is when i overextend i will throw up a wall in the opening closest to where i am that is the most likely to be the ganking doorway, for example if i am in mid and i feel like their team is coming from bot i just throw it in the brush leading to bot from the river and it will not only wall it off but it also gives sight in the bush and around it. Now for Glacial Storm,her ultimate, which is whenever you can of coarse, her ult does a decent amount of damage while they stay in it and it slows and once you Frostbite them it will apply the double damage so all in all great spell. As a side note, be advised that Crystallize is a hard spell to use, it took me a very long time to be able to wall just behind me. For example if i'm being chased by a melee and i use the wall just in time to block them, this is a very hard thing to do and i have seen sooo many Anivia's who try this and die because of it but it just takes practice and with diligence you will get better at wall placement.
Alright so just to wrap up i want to tell you all that both builds are viable on Anivia so it is really preference on which one you go with and the items can also be for situation use, also be free to mix and match the builds, the most important part of playing the game is having fun and what is the best way then to make your own build right? So get out there and ice some mice (you know cause birds eat mice?) and enjoy your Cryopheonix!
May 16,2012-Changed summoner spells, masteries, items and runes.
October 4, 2012-Added another build giving more option on what to build and updated the chapters. Not that this took WAY long since my keyboard is slowly dying and i have to copy and paste every single "u" and sometimes if the time is bad the "o" as well -_-.