Renekton is a fearsome melee dps, who can with a well time ultimate survive most fights and ensure that your team get's an ace. Instead of focusing on cooldown reduction as many other builds do, this will bring out Renektons great auto-attacking potential, which coupled with his stun can take down most champions.

Pros:

High burst damage.
Decent heal.
Decent escape mechanism.
Decent chaser.
Really strong in teamfights.

Cons:

Has a tendency to get focused down.
Is a really big target when ultimate is on.
Vulnerable to slows when slice 'n dice is used.

Quints and marks of desolation to increase his damage.
Dodge seals which increases survivability.
Flat magic resist glyphs to boost early magic resist, since you must endure alot harrass early.

Start off with Doran's shield to give you the required lane staying power. When you have 920 gold recall to buy Berserker's Greaves. If their minions is about to reach your tower you should consider using ghost so you can get most of the exp. Next item is Vampyric Scepter if you are having trouble in the lane but, if you are able to push the lane you should save up for B. F Sword. Then build The Bloodthirster as fast as possible. If you are able to stay alive The Bloodthirster is +100 AD and 25% lifesteal when fully charged, which will give your skills a good damage and healing boost.

Afterwards either get Banshees Veil or Randuin's Omen. I prefer getting Randuins because using its active will slow their entire team making them much easier to reach and it is both a great chasing and escape skill. Now your Bloodthirster should be charged up and u need a new item to keep your DPS increasing. For this I normally use Wit's End because it gives attack speed, magic resist and the passive melts mana users when Ruthless Predator is used.

If the game is still going build Madred's Bloodrazor to further amplify Ruthless Predator.

Early game

It is important to not be forced to solo lane and to lane with either a champion with lots of staying power like Malphite. Or with someone which can deal good damage at early levels.

Try to lane as aggressively as you can, but keep in mind that you'd like to keep your health fairly high. Renekton is at his strongest when they chase you into grass so once you're invisible turn around prepare Ruthless Predator, stun, auto attack some then use Slice to get away. Don't be afraid to push the lane to their tower as long as you don't take any hits from it, or if mid is missing. By using Cull the Meek for healing on their minions you can play one of the most aggressive lanes of all champions.

If they are playing patient and defensive so must you. Try to zone them out of exp range and let your minions die before last hitting.

When you have your ultimate you can towerdive most champions and get a kill before having to recall.

Rest of the game

If you got some kills early then you will now be one of the deadliest players on the team. When a fight starts don't attack untill your tank has gotten some of the aggro, then you must start focusing their carry/casters, use a fury charged Ruthless Predator, Cull the meek and start auto attacking if you need to use ultimate to survive long enough in the fight to get the kill. If you're being focused use Randuin's Omen or simply slice out at the lowest health possible.

Notes on playstyle

Some champions like Shaco or Leblanc who creates copies of themselves will drastically increase Cull the Meek's heal, and it will identify which is the real.

By luring a champion to attack you while you have little health, when both ultimate and Exhaust is ready you can score really easy kills by feigning weakness.

If a teamfight is not brewing using Ruthless Predator -> Cull the Meek -> Slice away before retaliation can keep their team on their back foot.