I decided to write this guide based on my experience from my low - level account, as i saw Tank Yi or some similar anomalies. This guide is recommended for those that just started with Yi, and i am pretty sure that you, the pro Yi players, have waaay better bulids.

Pros:
Very fast
Very deadly
Very dangerous if played right
Terror for AD/AP carries

Cons:
Squishy
Stuns counter you hard
Requires feed to be really effective

As you can see, we need everything for critical strike, armor penetration and damage. That is because Yi needs that and nothing else. Except for ultility, where we take reduced time dead (because being dead is the worst time in game), movement speed (Yi relies on being fast as hell)
and buff duration (as red buff is STRONGLY recomended)

Same as masteries - armor pen, damage and crit. Nothing special to say.

And here we get more complicated. As you might ask: "Why no damage items until IE?" That is because you have Wuju Style! That gives you all the damage you need. Other than that, take mainly attack speed and crit, and Banshee on end for some survivability and those bad CC.
You might consider Frozen Mallet or Trinity for that on - hit slow. I take Banshee instead for the spell shield. As for Bloodthirster/Hextech Gunblade - Both of these things are great on Yi, but need consider. Bloodthirster is flat AD and lifesteal, and Gunblade is to keep your Alpha Strike kicking, but adds less AD. Decide on your own.
If you face hard CC, take QSS after Emblem of Valor, and skip the thing you do not need.

Why Meditate last?
Well, because in my bulid it has no real place. This bulid is focused on killing everyone, not standing around and healing! And, your lifesteal will give you all the heal you need from minions only.
Why Alpha Strike first?
Harass, chasing, good early damage. Need more?

Flash: This is the best in - game sumonner spell. Escape, chase, wall jumping, this spell has it all.
Exhaust: This can counter other AD carries you need to kill first, as your main survivabilty comes from "kill before be killed".

Why no take:
Ignite - You are fast enough to catch them, you do not need this.
Cleanse - This is good for consideration, if you face hard CC. But in that case i recommend QSS, and Exhaust instead.
Smite - Take if you jungle, in any other case - no.
Heal - Good early, but falls off later. So, this has no real chance in long - terms.
Clarity - If you notice Yi is really mana - hungry, well that is true. But in long - terms, you will waste spell slot, that you can use for Exhaust that is viable all the time.

Double Strike: Your great passive. This saved my *** a lot of times, and I am happy for it. That double strike is twice the normal damage, so you can consider it as mini AD steroid.

Alpha Strike: Your main spell. Master this fast, as you need it for chase. Better explaining is in Farming/Harassing chapter.

Meditate: Well, i know about tanking potential for AP Yi with this spell. But, i play Yi as AD carry, so this spell has no real use for me.

Wuju Style: Main source from damage from early to mid game comes from this. ALWAYS turn it on right after you use Alpha Strike, if you attack enemy champion - not while harassing, but when charging head - on or chasing. (while the animation is still running, click E), as you will need that added AD. But be careful - when on cooldown, it is literally useless, as passive is off then. Think hard if to attack without it.

Highlander: This is what makes Yi so awesome. Massive attack and movement speed steroid on acceptable CD, and CD refresh for kill. Activate this the same moment as you activate Wuju Style for added power.

AVOID USING ALPHA STRIKE TO FARM EARLY!
This spell takes one hell of a lot of mana, and will leave you dry if you farm with it early. It is ok to do it later, but until you are around lvl 11, just no.

Harassing - As you may notice, you need to use Alpha Strike to do this.
But, DO NOT AIM ON YOUR ENEMY DIRECRLY, as Alpha Strike teleports you onto your target, if you won't kill with it. So, try to aim at minions! You get farm and your opponents get pissed. Profit.

Your role here is to wait for initiate, then Alpha Strike onto enemy carries with Wuju Style and Highlander active, and rip them to shreds. Do i need to say something more? Yes, be careful to attack after they spent their CC, as you will die from single stun without QSS.

Red buff is essential without Frozen Mallet or Triforce. Take it whenever you can.
Blue is important, and take it if you can, but it is not needed for survival.

So, i hope you get the basics. I will update this bulid according to your feedback.
(Also, if my bulid sucks, it is my first guide i wrote, so there is your reason.)