I bought Anivia at level 12, and have mained her ever since.
First off, I want to clarify that this’ll probably be pretty similar to a guide, but it is not meant for people who have never played Anivia before and want to start. This is to correct all of the idiots I see wasting Anivia’s potential and ruining their team’s game.
First off, what every Anivia player has to understand is that the blue buff was made specifically for you. No one else on your team should ever have it (except MAYBE swain). Your jungler should only need it once. Tell that amumu to man up and buy himself a frozen heart.
The reason for this should be obvious. Anivia’s skills cost a lot of mana. Without blue, Anivia can not farm, she’ll be completely OOM after a fight, and she’ll be next to useless until she has at least half of her ToG stacks up. Every Anivia player has been there (when a retarded Yi decides he’s more deserving of blue) and every Anivia player can tell you how much it sucks.
You can take blue as soon as you hit 6. Grab 2 health pots and a mana pot when you b. Go directly to the camp. QE, use 1 health pot 1 mana pot, R E (end R immediately after), QE, R(for the rest of the fight)EQEE. R uses up more mana for damage than Q and E, so those should be used for the main source of damage. Later, you’ll be able to just spam everything you have on it, and leave R up the whole time without running OOM.
Speaking of ToG, it should not, surprisingly, be your top priority in your build order. Although it is nice to get those early stacks and have an easy time avoiding mana issues later, it is often not needed, and can easily be taken later to the same effect.
Anivia should be in a solo lane. Anivia should be in mid, specifically. If Anivia is not in mid, she will not have easy access to blue, and your laning phase will be MUCH harder. If you’re feeling brave, however, you can coordinate with mid to steal their blue as soon as it respawns from their jungler.
As Anivia, you should not have to b until level 6, at which point you should have AT LEAST 30-40 cs. If you can’t reach this, you need to practice last hitting with Anivia until her attack animation is ingrained into your skull. Her animation is one of the most difficult in the game, though, so if you master it, you can last hit with anyone. Anyway, your starting items should be blue crystal and 2 health pots, for increased laning potential and cheaper build into catalyst. You should not harass not-ashe-ranged-carries/not-karthus-mages in lane (ashe and karthus are incredibly easy kills for Anivia) unless they’re clearly worse players than you, just farm up until you hit 6. However, if the opponent tries to harass you, don’t be afraid to q, then ice shard in the face. Also, get more aggressive if your jungler is planning a gank, but be careful not to push the lane.
Your first priority should be a Catalyst, due to its incredible ability to keep you in the lane for an extended periods of time (especially with blue buff), and its invaluable added early-game bulk. I see many Anivia players rush a RoA, however, I believe that the AP gain from that item is simply insignificant compared to the earlygame cost and your need for other items. Thus, after you get blue, you return to lane. Now Anivia becomes easymode. Just use r on all of the minion waves. Your waves will naturally push into their tower dealing damage to either it, or the champion protecting it. In the meantime, you have blue, so spam your q a bit to zone them from cs. You should have a ridiculous amount of money in no time, and you should be far and above the highest cs in your game. If you can afford it next time you b (after blue runs out) grab a needlessly large rod. This will boost your damage by a ridiculous amount. Boots are your second priority. After this, your build becomes sketchy. Oftentimes, I don’t get ToG until after my second blue runs out, by which time, I should have, or almost have, completed my deathcap. Get shoes when you don’t have enough for a larger item, the movement speed doesn’t make a huge difference with Anivia, but its still nice (the 20 mPen is DEFINITELY nice). After this, if the opposing team has some annoying stuns, grab a banshee’s veil out of you catalyst. If you want more AP get AA’s staff. If you’re crushing at any point in the game, don’t hesitate to grab mejai’s soulstealer. Nothing’s harder to kill than a fed Anivia.
If there’s a veigar on the enemy team, just build Catalyst, ToG, Boots, banshee’s, then AP. You’ll still be able to do significant damage, and the veigar will be next to useless.
In teamfights, your role is to AOE stun, drop your r in the middle of the fight, and jump in and out to hit with e and q whenever they come up again. Your wall is probably your most valuable teamfight skill, though. Learn to use it well ASAP. Don’t hesitate to test with it in normal matches, no one cares about how well you do in normals. Anyway, use the wall to block off escape routes, trap 2-3 enemies outside of what would have been a 5v5 teamfight (probably the best use of the skill), prevent enemies from following you, grabbing an extra point of mana every time you b (when you have ToG), and even prevent taking damage when killing golem.