Welcome to my Rengar guide. If really want to know why your building these items and picking these Masteries and Runes, read the notes attached. Otherwise, I'd advise at least reading the summary. Give this a vote if you find it helpful, thanks!
- Spin 4 TR8Rs

P.S. I'll update the Counters list as I play Rengar against more champions in ranked. Feel free to comment your experiences with Rengar below.

You want to build Rengar as mobile as possible: The mobility will help you dodge binding/slowing skill shots, close gaps, and escape from enemies. Additionally, the extra movement speed allows you to pop your Thrill of the Hunt (R) from much further away and still reach your target while still invisible. The advantage of this is that they wont know that you've used your ultimate until its too late, as well as, give you an opportunity to change your mind if the situation is not ideal and escape.

You want to build Rengar with as much flat AD as possible: Rengar is like a drive-by shooting: you hit them hard, maybe kill one or two, and get out; you're not looking for an extended fight. Consequently, you don't need to build attack speed or on-hit life steal; it's not worth it. Rengar's kit simply does not give you space to drag out duels, especially if they've built tanky.
Your Masteries and Runes should reflect these two strategies.

Although it is a lot of fun to go straight AD and jump from bushes, it's not reliable. You wont help anyone if you die every single time trying to assassinate champions left and right, you'll just feed the opposing team (and therefore lose more often).
This is why I advise taking him top: you wont have to worry about ganking other lanes and/or missing farm. You'll have a consistent gold flow if you farm well, which is especially easy using Rengar's Savagery to last hit. Additionally, the 1v1 scenario top, with the lane's bushes, is ideal for Rengar's play style: you can hide in the bushes and use his Unseen Predator to harass enemy laners with Savagery and last hit minions without worrying about getting blocked by other minions (It happens to all of us).

Play it safe top lane until you get a little practice with Rengar. Once you start getting a feel for the range of Unseen Predator and when to use your Ferocity, you'll see that killing top-laners isn't that difficult. You'll find that OTHER top-laners are often very stubborn and if YOU are patient, you can get a solid 4-8 kills out of them before having to group with the team.

Use your Teleport to help other lanes once you've gotten your fully upgraded boots and at least one complete item (Preferably two).
GOOD LUCK WITH KNIFE KITTY!

1. When chasing an enemy often times your Unseen Predator will provide you with the necessary gap closer. Look for nearby bushes to catch up to champions that have flashed or are simply faster than you.

2. Even in fights where you are the weaker opponent, fighting in bushes will give you the advantage you need (especially the three bushes lined across top and bottom). If you can draw your opponent into this space, you will be able to constantly poke them while sustaining the least amount of damage. You can do this by first getting ahead of them by at least one bush. Once they walk into the open space between the bushes, jump, use your Savagery, and run into the opposite bush. Repeat this process for best results!