Here is a brief Kha Zix guide.
Max order: R>Q>W>E
Evolution Order: Q>E>W
Situational Evolution Order: E>Q>W
Jungle Build: Lizard, black cleaver, boots(Ninja, mercury, or mobility), Ravenous Hydra, last whisperer, Guardian Angel
Mid Lane build: Black cleaver, boots(Ninja, mercury, or mobility), Maw of malmortius, Ravenous Hydra, last whisperer, guardian angel
Situational items: Bloodthirster, Banshees Veil
While playing Middle Lane Kha zix, you want to go aggressive after level six and evolving your q. The reason you evolve q first is because without it, you don't have much damage. The reason you want to evolve e second is because of the resets on kills or assists, and more mobility. Once you either win lane or hit 11, you want to roam and grab objectives or gank lanes. During the late phases of the game, wait for someone to engage a teamfight, then go in for the ad carry or whoever is squishiest(Least health). Once you kill them, just keep using your e resets to kill more people. The good thing with kha zix is that he also fits the role of a fighter(to some extent). So don't worry if your in the middle of a teamfight, just lay on more damage.
While playing Kha zix in the Jungle, if your having a hard time ganking evolve e first, but i don't recommend it. Just hit level 3 and try to gank the lanes. If you can't, just hyper farm the jungle till you hit 6. Kha Zix is also good at grabbing dragon early with 2-3 team mates because of the heal from his w and short cooldown on his q. Late game if you have full build, you can sell Lizard and get a banshees veil or maw of malmortius. If you are very ahead mid game you might want to consider buying a bloodthirster.
Anyways, I know I rambled on a lot, but that's pretty much all you need to know :P. Good luck on the rift!