Hello guys,
First of all this is a build I play for fun only. I don't know if it will be viable high elo, played lots of successful ranked games though. Please see playstyle section for pros/cons and teamwork. First four items(deathcap boots and lichbane) are my core build rest can be arranged according to the game.

Runes are pretty straight forward I think.

Caster masteries. You can go 9/21/0 too if you're new to yi, since he is freaking fast and easy to do mistakes.

Ok, this is tricky.

For laning phase:
Harrasment and farming is very important. You can take mid or duo lane against any opponent easily. If they're too tough just play more def. Here is what to do: Use alpha strike when there are 3 or less minions. Use alpha strike on minions to harrass. If you use it on champs you can get harrassed too which is not a big problem cause you can meditate and continue but its still dangerous early game. Don't try to rely on your auto attack but don't underestimate it either.

For teamfights:
This is where ap yi gets a little hard to play. You have to seek for the opportunity. Wait for your team to focus one squishy. Watch all the enemy players HP. When you see one of em going down, pop ulti and alpha in. If it won't go down, probably you will. So knowing your damage and timing your alpha strike is everything. You can still meditate and hold on in the middle of a freaking fight, till you get stunned etc. That would be the worst scenerio. If you can manage to time your alpha strike correctly, you can just pop ulti again and look for the lowest health enemy. In some fights, you can repeat this 4 times which leads to pentakill without getting any damage since you will be invisible most of the time. Always try to poke em when enemy creeps are right in the middle of two teams. Alpha strike to last minion of the wave. Only way to avoid this poke is to stay far away and this fact makes this move very defensive as well.

Using summoner spells:
Got clarity for several reasons. You can use it as heal as well since your Meditate ability scales amazingly with ap. Yi has tiny mana pool if fight lasts long you will either be dead or useless. Cleanse is just amazing because when you start your ulti+alpha combos in a teamfight they will try to cc you. They can't slow you down ulti prevents that and can't stun you now with cleanse.

Lich Bane:
Well, since this is an ap build your Wuju Style ability is rather useless. Lich Bane eliminates this. Just alpha strike in, slap two times, use Wuju, slap one more. So what does this mean? Lich Bane has 3 seconds of cooldown for the bonus damage passive. Instead of not using Wuju Style or wasting by using it too early, you use it 2 seconds after you hit them with Lich Bane. Ap yi uses Lich Bane twice when attacking and this leads to devastating damage if you have high ap which is not an issue because ap yi farms extremely well.

Farming:
Just farm like crazy. Go clear jungle if there are no minions close. Constantly get gold.

Buffs:
Blue buff is everything. Always try to get it. It makes your alpha strike spammable and if your clarity is cooldown it helps a lot.

Pros/Cons:

-Pros
Amazing burst damage
Big potential to have triple quadra and pentakills
Hits hard after alphastrike with lich bane
Pretty annoying since you can heal in the middle of a fight with 1:1.65 scale on meditate
Good harassment
Effective both early and endgame
Can be a game changer
Incredible farmer

-Cons
Very bad on 1v1
Blue buff dependant
Can be useless in some team formations
Banshees Veil can stop you easily