This build has done for me WONDERS!

Now the first champ I ever bought was Yi, but then I moved to Warwick and Rammus because "The" Tier List said Yi was T3...every champion in this game is viable it only depends on the player.

I recently came back to Yi and I have destroyed entire teams without passing my 3 kill bar...almost always being the highest damage dealer even against teams with Vlads.

You should have it like this...
Crit Chance: Armor penetration only really comes into play at end game...so crit chance is better for you early on.
Dodge: Because sometimes you just need to DODGE!
Focus: Self explanatory.
Swiftness: Trust me...you need to run your *** off.

This build helps you all around...movement speed, for your Q, Mana regen and pool and the ever so important Summoner Spell 15% CD.

The role of the Backdoor is a MUST in every game. Some people might say but your team will be doing 4v5! MISTAKE! Your team will be fighting 4v3 or even sometimes 4v2.
This build lets Yi DEMOLISH 1 on 1 mostly everyone.
You will cut down the lone person they have to defend their turret and they will be forced to employ 2 or 3 people to stop the backdoor and this in turn will let your team rampage through lanes.

To do this you must have SOLO Lane. I know, I know: Solo lane for a Yi? Nonsense! Irelia! Tryndamere! They all own Yi!
Trust me with your Q harassment you can hold your own even against range laners such as Ashe or Swain.

Getting Avarice Blade first is a must, some may be tempted to get Vampiric Scepter but you don't need it. Once you get it and with your farming ability the Youmuu's and Berserker's will come fast.

Don't die! Use exhaust! Use Ghost! Don't be shy!!! Your 15% Summoner Ability Cooldown Mastery is there for just this.

If you've done your job(Activating everything and destroying turrets) right you should have been able to take down the first turret now here's what you must do...STAY on that lane! People always go: "Well turrets gone...let's see what everyone else is up to!" MISTAKE!
You keep pushing that because people will leave it. Try to make different appearances throughout the map but always go to that lane and DO NOT go into Team Fights...you WILL get clobbered.

Early game with your Youmuu's Active + E + R you will be slashing through things like you had a Phantom Dancer and *insert popular damage item here*.

Mid game no one can stand toe to toe with you 1 v 1...why? By now you should have Sword of the Divine and Wriggle's.

Wriggle's is a must to avoid getting ganked. Brace yo' self foo'! Ward your escape route.
Also Youmuu's, R and Ghost are your Escape Mechanisms...so again DO NOT BE SHY!

SoTD is a JAX killer and a "Damn lucky dodge!" avoider. In order to kill champs you MUST throw everything out and quickly! F (Exhaust), 1 (Youmuu's) + 4 (SoTD) + E + R = Kill!

By now it's end game and your enemy team will start screaming: "TURTLE, TURTLE!" So you need Reverie's and Quicksilver Sash.

Reverie comes first because of Philosopher's stones 5+ Gold. It helps. Now with the 40% Speed Buff you will have a 4th escape mechanism!! Plus The CD with Youmuu's and your runes and masteries will get you near 40%.

Quicksilver Sash...how I love this item. It gets me out of any jam...I won't even go into detail just...try it.

If your team does the job right and they go top while you bot or they bot while you top...it'll be over quickly.

Invisible Champs. After you get Youmuu's and Berserks you MUST get an Oracle. Then continue with the normal build and if you die GET THE ORACLE! These will be the champs they're gonna get to try and get you to stop backdooring first.

DOT Champions. Usually they think once they get a Dot on you and you run that you will die...they USUALLY do not chase so get in a Bush and W your fanny off!

Greedy Wankers. Sometimes you will be involved in a team fight and they will want to kill you for all your backdooring so once you're low in health try to run and if you just can't escape then head to your nearest ally and W!!
They will focus on you but with your 700+ HP in 5 seconds and the 300 Armor and Magic Resist throughout will let your ally get in the hits he needs to actually be able to take them out and with a good possibility that you will survive this ordeal.