Hi there, welcome to my Rengar guide. Rengar is very fun and challenging champion to play in the League. Using the wrong skill when max charge can mean the difference between life and death. I'v noticed that a lot of Rengar guides tend to focus on leveling up Savagery first, something I have only done once with terrible consequences. Well, let's get to it.

I run ArP, Armour and MR runes. Feel free to use the MR per level instead of flat. Also, AD instead of ArP would be fine, perhaps even better but I am not willing to spend the rediculous IP to get runes that won't make a huge difference in a game.

I think that Executioner is a total waste, but feel free to take it. I like a standard 21-9, or a 20-10 for jungling. Taking the extra cooldown % in the Offence tree since cooldown time is the only thing that your abilities depend on.

Ok, the most important part, Items. Now, I like to play Rengar in an assassin type role, I find other than harassing with Bola my fights tend to be short and sweet. Get in, kill my target and ult out to run or to buy some time to choose a new target and jump back in. For this reason, I chose a cheaper build with a couple active items.
I start with boots and potions x 3. I then move into building towards YouMuu's Ghostblade. I feel like this item gives you an amazing active ability that can really turn the tide in early fights and get some stacks on the Bone Necklace. I build the Brutalizer if farming is going alright and I am getting the upper hand or breaking even with my opponent and I build Avarice Blade if I am getting out farmed (shouldn't happen after you read the next section). Get the Bone Necklace before YouMuu to build stacks or just go YouMuu if you are behind and would be unable to get stacks without it. REMEMBER TO USE THE ACTIVE!
Boots... well, there are two boots you may want to get, personally I like the Swiftness boots, but many game I need to get Merc Treads. You can really get shutdown by silences and other CC abilities.
Since Rengar scales on AD, build AD. His built in heal is nice early but build some lifesteal in as soon as possible after YouMuu while you are saving up for some AD. I like to take Spirit Visage because I feel like Rengar benefits from every stat it gives and it is cheap. If you have lots of Money feel free to get something else to hit harder but this item is a good choice as it allows more abilities to be used (cd%) and more healing to be done at the same time. Your final item can be anything, Guardian Angel, Hextech Gunblade (PROVIDED U USE ACTIVES!), Infinity Edge, Phantom Dancer or Black Cleaver.
Let me explain the obviously strange choice - Hextech... Rengar's 'w' ability uses 100% Ability power so you are adding 70 Magic Damage to your AoE ability late game not to mention you can deal an additional 300 Magic Damage to your target AND slow them. Remember we are trying to take out the carries and Hextech gives sustain, damage and an added slow in case Bola is not up or a little bit of damage to finish them off. Still, often the other items may be better simply because many people forget actives, and it can be difficult to hit your target with them. I try to lead with it and save Bola for when (if) my target flashes or runs and slow them again.

Skill sequence is the reason I wrote this guide. Every Rengar guide seems to level up Savagery when in reality doing so does not significantly increase damage or lower cooldown at all. The other abilities do get decreased cooldowns as they level up. The other reason I leave Savagery until the end is that you mainly should be using it when you have max stacks of Ferocity, in which case the bonus damage has nothing to do with the level of the ability, but rather your AD. The final reason we level up Bola Strike first is that Rengar cannot harass without it. Unless you are always jumping from bushes to land Savagery, you don't have a harass. Level up Bola, harass the enemy, and enable easier farming. If you can make it to mid game with a decent farm, hit the jungle, stay near your team and take out the important target when the opportunity arises. Use 'q' when full Ferocity, (or 'e' for the stun if the target sees you coming or you have teammates their that are going to help you take them down). Don't use your heal mid fight. 15% hp is not going to save you. Killing your target is far more important, damage equals lifesteal equals healing. Do not use 'w' with full Ferocity unless you are alone in the jungle and trying to get to a safe place to recall. It's not worth it.

So, sorry I haven't looked into adding pictures of items. I don't care really, I am just trying to help people understand that Bola Strike is the real weapon of Rengar early game and allows him to become unstoppable later on. Hope you got through the text. Please vote based on content and not on the presentation, I realize it is lacking. If anyone would like to spruce it up, feel free to do so. Please just give me credit. Thank you and have fun. But don't get hopelessly sucked in and ignore the many other great things life has to offer. A life on LoL is no life at all.