Renekton is very strong early game.
From level 1-6 try to make your opponent scared and try to deny them CS.
Don't go too aggressive until you reach level 6.
At level 6 there is a possibility that you could get ganked so be cautious.
However if you're safe from a gank then try and go for the kill.
I don't recommend using your ultimate too early into the fight because if you do it will scare them off.
Save it until you are both quite low as this should secure you the kill.
At level 8-9 start roaming a bit to help out the other lanes.

Mid game renekton is very strong, if you have played the laning phase correctly then you should be a bit ahead of every other champion, so therefore this stage in the game will make or break Renekton.
You should try to pick up as many kills as possible and try to get as far into the build as possible mid game.
This is because renekton needs to be tanky but he also needs to have damage, so thats why i recommended starting with the brutalizer, but then getting a Frozen Mallet.
In my opinion Frozen mallet is the best item to get on Renekton as it gives you a good amount of damage as well as giving you health.

If everything has gone correctly so far then you will be virtually unkillable at this point, you should be close to finishing the build and hopefully have 8+ kills with maybe 4 or less deaths.
Renekton is very strong in team fights because of his ultimate. He also has good AOI range/damage with his Q and E. Renekton is different to an assassin because you don't want to get out as soon as possible, if you're build is correct then you want to try and take all the damage and do your best to product the AD Carry.
If the opposing team if smart then they will target the AD carry and Renektons job is to use his W to stun and let the AD carry get away or get to a safe distance to still do damage.

Start W and do your best to last hit. But when you get to level 5 or 6 then your Q should almost one hit minions, so if there is a big wave of creeps then do a little bit of damage to them all with basic attacks and then use the Q to hopefully pick up 8 or 9 CS.
However, unlike many top laners, CS isn't crucial to playing a good Renekton.

Overall
Renekton, is one of the best champions in the laning phase.
Usually all champions that are strong early game, fade away and stop being so effective late game, but renekton is different.
However doing well in the laning phase is crucial to playing a good Renekton.
If you don't get ahead or get a few kills before 15 minutes then Renekton won't be quite as effective.
When you get to level 6 you should always go for a kill, this is because when you have activated his ult you are able to take a few turret hits if needed and secure the kill. Later on in the game, maybe when you get to level 8 or 9 try to start roaming a bit to help the other lanes out.
You are able to do this because Renekton doesn't rely on CS.
In team fights try to take all the damage and protect your team.

If you're behind in the laning phase then ask the jungler if you can take control of the Golems. This is because they are crucial to getting your self back into the game as they will give you the well needed Gold and XP.