Through this build you will see that having a stunning, rage-induced, gator in your line-up is a great team boost. I will go over items, runes, masteries, skills, and spells along with all their reasons. The laning how-to's and omfg my team sucks what do I do will also be discussed in later parts.

Reign of Anger
A champions version of Roid-Rage
Cull the Meek
AOE damage plus healing yourself? Get in range of champions and it's 4x stronger? A fantastic heal/farming tool. I level this along with Slice and Dice to do real damage.
Ruthless Predator
STUNLOCKED! Get this first but level this last because the stun stays the same all the way through. Even though you get a flat increase in damage it is not the way to go.
Slice and Dice
Get in, do damage, get out. This also has an even funnier use. Double dashing past minions to last hit the champions who think they can get away.
Dominus
Any reason why you wouldn't want more health, damage enemies per second, or gain fury to hit harder? The best part of this is that its all magic damage. When enemies stack armor against you, Dominus makes them pay for their stupidity.

Doran's Blade
Doran's blade is a great item to start the game off. With a little life steal, extra damage, and a lot of health, the blade makes you less squishy and more laneable.
Berserker's Greaves
Shoes are a must early game to help you stay out of ganks, push for last hits, and since you get extra attack speed with these fools, better hitting power.
Phantom Dancer
YOU MUST GET THIS OR YOU WILL FAIL. No questions asked. This is your biggest help playing Renekton who hits super slow. The crit will help you late game, and the movement speed just makes you a roid-raging, NASCAR speed, champion eater.
Bloodthirster
OMG LOL WHAT? You get extra damage and a huge boost in life steal. This is your staying alive tool. Without it, you can do lots of damage, but they can just turn and hit you. Even if you get into a fight against an actual Yi (I do recommend 1v1) you both can just sit there and see who right-clicks faster. Since you have a stun, a heal, and a auto-attack breaker, you should win unless your bad.
Infinity Edge
Well... quadra-kills and penta-kills are gonna happen <(^^)>. Lots of damage and enough critical strike to make you hit a crit every two hits. Oh, and you'll be hitting for about 600 every crit.
Black Cleaver
MOAR DAMAGE MOAR SPEED and yes rip armor to shreds. Even a Garen with a Thornmail will fall to your might.
Frozen Mallet
When you have completed your first 6 items its time to get rid of your Doran's Blade and substitute in the worst thing for your enemies. You will gain 700 health (no more squishy) and add 20 damage. The passive is what makes your day though. A slow. You may now beat the **** out of anything without the fear of it running away... cuz it can't LOL.
Phantom Dancer
Shed your croc feet of them shoes and get another dancer. You still run faster than anything, but now you hit faster and with more crit.

Greater Mark of Desolation
You do Physical Damage thus you must have Armor Pen
Greater Seal of Resillience
You be squishy mate, armor helps keep hits from hitting too hard.
Greater Glyph of Scaling Magic Resist
Karthus, Veigar, Ezreal, and Lux all could just AP dump on you so you need some sort of resistance. I chose the scaling one because late game is when you should be worried about it.
Greater Quintessence of Desolation
Because you can never have too much Armor Pen.

21-9-0
Extra Crit, Armor Pen, More Damage, healthy armor and magic resist. Its a Killer waiting to happen. Take note that I did not get the extra AP from Ignite. It is not enough to give you any damage to your ult so don't even try to get it. Extra Minion Damage works.

To be perfectly honest, use them as cannon fodder. Each of your teammates will do a bit of damage and get some enemies low. Go round the back and just own faces. Quadrakills and Pentakills are well within your grasp if you don't get hard targeted by the whole team. After wards just go hit a tower or solo dragon and baron to hit harder.

Slice to the middle of all minions, cull the meek to hit them all, and dice out. Against two enemies, make sure your partner knows who to focus and who to harass. Once they are harassed low enough (1/4-1/2 health) slice in, stun, cull the meek, dice to them again. If need be use your exhaust and ignite when you feel it necessary.