Renekton is a interesting champion. Although he is large, he is quite squishy, meaning you need a combination of damage, tank items and cooldown reduction. Since Renektons abilities have no cost CDR is very useful for harassing. The build order doesn't really matter, it depends more on how the enemy teams play.

(the skill details were copied from http://www.leagueoflegends.com/champions/58/renekton_the_butcher_of_the_sands)

Cull the Meek - Renekton swings his blade, dealing moderate physical damage to all targets around him and heals for a small portion of the damage dealt. If he has over 50 Fury, his damage and heal are increased.
Renekton swings his blade, dealing 60/90/120/150/180 (+) physical damage to nearby enemies and gains 5% of the damage dealt as Health, up to 50/75/100/125/150. Each hit grants 5 Fury, up to 25. Enemy champions grant 300% additional health recovery.

50 Fury Bonus: Damage increased to 90/135/180/225/270 (+). Heal percent increased to 10%, up to 150/225/300/375/450.

Cost
No Cost or 50 Fury
Range
20

Ruthless Predator - Renekton slashes his target twice dealing moderate physical damage and stuns them for 0.75 seconds. If Renekton has over 50 Fury, he slashes his target three times dealing high physical damage and stuns them for 1.5 seconds.
Renekton's next attack strikes twice dealing physical damage (10/30/50/70/90 + 150/150/150/150/150% of his Attack Damage) and stuns for 0.75 seconds. Each hit applies on-hit effects.

50 Fury Bonus: Instead, Renekton attacks three times dealing physical damage (15/45/75/105/135 + 225/225/225/225/225% of his Attack Damage) and stuns his target for 1.5 seconds.

Cost
No Cost or 50 Fury
Range
300

Slice and Dice - Renekton dashes, dealing damage to units along the way. Empowered, Renekton deals bonus damage and reduces the armor of units hit.
Slice: Renekton dashes, dealing 30/60/90/120/150 (+) physical damage. Hitting an enemy grants the ability to use Dice for 4 seconds.

Dice: Renekton dashes dealing 30/60/90/120/150 (+) physical damage.

Dice - 50 Fury Bonus: Damage increased to 45/90/135/180/225 (+). Enemies hit have 15/17.5/20/22.5/25% reduced Armor for 4 seconds.

Cost
No Cost or 50 Fury
Range
25000

Dominus - Renekton transforms into the Tyrant form gaining bonus Health and dealing damage to enemies around him. While in this form, Renekton gains Fury periodically.
Renekton surrounds himself with dark energies for 15 seconds, gaining 300/450/600 Health. While active, he deals 40/70/100 (+0.1) magic damage to nearby enemies and gains 5 Fury per second.

Cost
No Cost
Range
20

Reign of Anger - Renekton gains Fury for every autoattack he makes. This Fury can empower his abilities with bonus effects. Additionally, Renekton gains bonus Fury when he is low on life.http://www.mobafire.com/league-of-legends/edit-build#

Using these skills, renekton is awesome at two things early game: Harassing and farming. Since he can always heal himself with Cull the meek, he can remain in lane for a long time while killing lots of minions for gold. With Slice and Dice, he can jump to the enemy champion, use another skill and then jump out. Ruthless predator is great for damage, the stun it gives, in ganks and teamfights. With his ult he can more easily turret dive because of the health bonus it gives.

A very important thing to remember is to cast cull the meek whenever you can, for damage and healing.

As mentioned in the introduction, the order in which buy the items matters more on the enemy team than anything else. He is a hybrid between tank, DPS and CDR.

My first item is always Dorans Shield, because it gives me a nice health, armor, and health regen boost early game.. some say that it sucks since it became more expensive, but I find it still pretty nice with him.

After Dorans sheild, i get to ionian boots of lucidityas fast as possible for the movement speed, and the the much needed CDR. Since Renektons abilities have no cost CDR is very useful for harassing enemy champions.

Spirit visageis a must have when playing renekton. It not only beefs him up, it gives him CDR. The main reason is because it stacks with the heal from Cull the Meek
The next item is Brutalizer.This is a great item as it gives CDR, damage and armor pen. With this your abilities deal a lot more damage and gives you the maximum amount of CDR with masteries. With the extra armor pen, you deal more damage to your foes.

At this point, the order in which you get the next items is completely up to you. Usually, I take black cleaverfirst for extra damage, attack speed and armor pen. You won't need anymore attack speed than this. And it stack with ruthless predator.

At this point i sell dorans shieldto make room for Frozen mallet

I take Frozen Malletfor extra health, the slow and the damage. This is a good item because it make it easier to chase down prey with ghost and exhaust.

By Frozen Mallet, the game is usually over, but if it isn't, then get a sunfire capesince it stacks quite well with your ult as well as beefing you up even more.

If the game is still not over, my final item would be replacing the brutalizerwith youmous ghostblade

This is why he is so great. Because of the heal from cull the meek and spirit visage, he can be in lane for a very long time. since cull the meek also deals damage he can just wait till the minions are low on health and get lots of gold with one cull.