When you first start off, you want to go to blue buff, it will give an extra ten percent cooldown reduction, which will help with early game bursty ganks. You follow up with wolves and wraiths, pop as many health pots as you need. Now, once, you get your red buff, gank a lane with an overextended enemy. You should be at least level four. Early game ganks will get you fed, due to rengars early game bursty abilities. For the most part, whenever you look to do serious burst damage, you build four ferocity stacks, then you press "q" once and then autoattack, press "q" right after that while autoattacking. Rengar's main issue is that he struggles to keep up if he does not have gold from kills. Take advantage of people that overextend in their lanes, and get that needed gold. (Also, just read your abilities it helps with every champion you'll play. Just do it...)

Most of Rengar's power carries over from early game to mid to late game. So, if you do struggle in the early game, you no longer have the luxury to buy these heavy ad items. Rush the tanky items I've shown, and then build ad items. Otherwise, you'll end up feeding and nobody wants that :)

Team Fights are so good for Rengar. If you have all the items, all you have to do is pop your ult and then find the ad carry or maybe the ap carry, burst them down with your q.q combo. (did you see what i did there? :3) But seriously, just press q twice with four ferocity stacks while autoattacking. In the end, you should have a kill, and due to the tanky items you bought you most likely won't die.

Now, assuming you beasted in the early game, you should buy Ravenous Hydra and Phantom Dancer. This is a great strategie for late game Rengar. You find a lane that's free of champions and that is decently pushed out on your side. Your "q" and "w" abilities with your Hydra and Phantom Dancer will clear waves so fast it's not even fair. Once you're through those minions build four ferocity stacks and burst down the tower in five seconds and maybe even an inhib. But, you must have vision on the enemy team whether its by teammates or by wards you need it, because right before you get caught, you can pop your ult and ghost to get past the whole enemy team sometimes. (Trust me, I've done this, it works enough said...)

Pros:

If you went ham in the early game you will have crazy burst damage, and great split pushing ability.
He can be the off tank for your team, with these items.
He is a great chaser, almost always he will be able to secure kills that other wise would have been lost.
Late game he can push lanes EXTREMELY fast!

Cons:

If you don't get the items in time you will fall off and be forced into a tank role.
Rengar WILL get countered with hard crowd control there is nothing you can really do about that though.
He requires much more vision when engaging, while his passive will provide you extra range, it can force you into sticky situations you didn't even know about.