So this is a short guide to show you that anivia is still viable. This is the ancient frogen's build, when he played anivia. Sure this get nerfed but it's still pretty good with a bit of skill. This is based on your mejai. Tear and ROA will give you enough mana (even if you need blue of course) to spam and kill and warmog and ROA will give you health to surviv and don't lose mejai' stack ( the egg is way harder to kill with 3000 hp).

first i'll speak a bit about her skills:

passive : Rebirth STATIC COOLDOWN: 240
Upon taking lethal damage, Anivia will transform into an egg with full health. While in egg form, Anivia is unable to make any actions and her armor and magic resistance are modified by −40 / −25 / −10 / +5 / +20. If her egg survives for 6 seconds, Anivia is revived with the same percentage health that her egg had.

---> This is really usefull except if you go rambo 1v5 but if your team can def you it's convenient. Make sure to have your egg ready before trade in laning phase.

Q) Flash Frost RANGE: 1100 COST: 80 / 90 / 100 / 110 / 120 MANA COOLDOWN: 12 / 11 / 10 / 9 / 8
FIRST CAST: Anivia launches an orb of ice in the targeted direction, dealing magic damage to any enemy it passes through. At maximum range, Flash Frost will detonate automatically.

SECOND CAST: Anivia detonates the orb, dealing magic damage and Stun icon stunning enemies in a 75-radius area for 1 second. Enemies can be damaged by both parts of Flash Frost.
MAGIC DAMAGE: 60 / 90 / 120 / 150 / 180 (+ 50% AP)
MAX. DAMAGE: 120 / 180 / 240 / 300 / 360 (+ 100% AP)
MISSILE SPEED: 850
Enemies damaged by Flash Frost are Chilled for 3 seconds, Slow icon slowing their movement speed by 20%.

---> This is only an utilitary skill to make good gank, run away and have some cc. It'll help you to kill as it up your E and allow to use your ult for a longer time.

W)Crystallize RANGE: 1000 COST: 70 MANA COOLDOWN: 25
ACTIVE: Anivia creates an impassable wall of ice at the targeted location for 5 seconds, perpendicular to which way she's facing. The wall grants sight in a large area around it.
WALL LENGTH: 400 / 500 / 600 / 700 / 800

---> This is also a utilitary skill but it's way more usefull in teamfight to spit the advers team or to catch someone. It'll help you to stun too.

E)Frostbite RANGE: 650 COST: 50 / 60 / 70 / 80 / 90 MANA COOLDOWN: 5
ACTIVE: Anivia sends a shard of ice at the targeted enemy, dealing magic damage.
MAGIC DAMAGE: 55 / 85 / 115 / 145 / 175 (+ 50% AP)
Frostbite deals 200% damage to Chilled targets.
CHILLED DAMAGE: 110 / 170 / 230 / 290 / 350 (+ 100% AP)

---> this is the "best" skill of anivia and it hurt really hard. you should always use it after stun or slow with your ult so it make double damage.

R) Glacial Storm RANGE: 615 COST: 75 MANA + 40 / 50 / 60 PER SECOND COOLDOWN: 6
ACTIVE: Anivia creates a blizzard at the targeted location. Enemies within the blizzard take magic damage per second, and are Chilled for 1 second, Slow icon slowing their movement speed and attack speed by 20%.
MAGIC DAMAGE PER SECOND: 80 / 120 / 160 (+ 25% AP)
Anivia can re-activate Glacial Storm at any time to disable its effects, and it will deactivate automatically if she gets too far away or runs out of mana. Additionally, Glacial Storm will be deactivated by all forms of interrupting crowd control, excluding fear and taunt.

---> this is your principal skill to farm. it's usefull in teamfight because of the aoe damage but stun or silence delete it...

they are pretty usual runes for a midlane but if you are playing against an ad mid you might have to take armor seals.

It's better to take your stun lvl 1 in case of an invade , to help your jungler and also bescause your E ,without Q or R is useless. Then it's usefull to up your E, it's your principal spell, you will play around it to try to double damage. Then you can choose to up Q or Z; i prefer up Z because your wall is bigger and it's better to play in team but if you want more damage up your Q ( it doesn't make a longer stun). Of course up your ult whenever you can.

First buy a doran ring and some pots but if you are against an ad mid a cloth armor. Then go as fast as possible into your tear of the goddess and then your mejai. If you have enough money to buy your mejai at first back do it. Think about your boot and go for a ROA. Once you have done it you should have enough ap for the mid game so go on warmog to have hp. Then go on your archangel that you should have reached the 750 mana. Finish your stuff by a rabadon. Anivia doesn't need much ap to hurt so if they have many magic resist you can go for void staff. if they are all ad you could take zhonya or abyssal if they are ap.

I recommand flash and ignite. Flash is really necessary as long as anivia don't have much mobility and no escape. Ignite is nice to take kill so if you have a good match-up take it.

You can take exhaust if you aren't sure of the match-up.

You can also take ghost cause anivia is one of the slowest champion.

You could take teleport too if you want to farm.

rest aren't that usefull.

Anivia is able to kill or at least farm almost all champ except those who have a stun or silence (it stop her ult) or mobility because (hard to hit with stun but not horrible to play against) so you should maybe don't pick her against kassadin, talon, ahri, zed, yasuo, fizz and lb. or take exhaust and just farm and play def.

After lvl 6 it's really easy to farm with anivia. Just put your ult in the center of the wave and then use your stun. before 6 it's way harder as long as anivia don't have much ad and a really slow attack animation. Don't hesitate to use your E to finish a creep.

Bleu is a really really really important buff for anivia! she is quickly out of mana so try to take the second. Your ult cost 70 mana and 40/s at 1 lvl so you need the blue and it'll help you to charge your tear.
If you play against a good team you should ward your blue in case of a steal from their jungler.
It's easy to do the blue as anivia; just stun him, then put your ult and your wall, he will stay at his place and won't attack you.

As fast as you have your mejai try to make kill. Call your jungle or to a gank bot/top or even invade with your jungle. And try not to die. in teamfight you will stay at the back and spit the front lane of their team from their carries. So you can kill their front lane with a good ult and then go on their carries. Try to fight in little passage where it's easy to put a good ult/stun/wall.

Well that's all you have to know to try this build or this champ. Hoping you enjoyed it don't hesitate to let a comment and see you soon on the battlefield with your bird!

PS: sorry if there are many faults of english, I don't come from england.