As Kha'Zix you will want to be aggressive early, he is a high risk champion with good damage output till level 3, if you fail on your aggression early and you die then you are in trouble but if you successfully kill him at first few levels you can start snowballing from there. Also Kha'Zix gets outclassed by most top laners so getting that small lead is important and remember that your worst levels are 4-5 that's your weakest point in the early game. Junglers are your worst nightmare, you will be aggressive so the target will be on you just pay close attention to your enemies movements to know if the jungler is on his way or he is already there waiting for you to get baited.
Mid game is where Kha'Zix shines, ideally you would want to be level 11 with , with these items you can go say hi to the enemy mid laner by applying a lot of pressure. Just 1 > > can either blow his right away from the damage he will suffer or if he doesn't have there is a big big chance the enemy will die.
At this time killing a wave of creeps takes ~3 seconds, you auto attack all melee creeps once and use to kill them all at once giving you a lot of time to do whatever you want after
In case you are behind and you haven't been able to grab that yet then farm up with as much as you can, sometimes it depends whether you can kill all caster minions with just 1 or not depending on your level and your items at that time. When you first grab you will be able to kill the caster minions with just 1 for sure, you will also see a big difference on your damage output that most of the times is unexpected by your enemies
If you are forced to join a teamfight(dragon and even baron sometimes) or a skirmish, it would be optimal to have your first, if you don't then its ok your damage output is still something to be afraid of.
Late game is the time where baron fights start happening and in general lots of team fights. Pick targets before fights and have them as priorities, usually the order of your priorities is:
AD Carry > AP Carry > everyone else
There are exceptions though, sometimes the enemy AP Carry might be scarier than the enemy AD Carry so you change that order, its up to you and your judgement.
In team fights you play the role of an Assassin. You want to wait for the best time to go in and start cleaning up, you wait wait and wait till most people have used their ultimates/CC's so that you have an easier time going in and killing anyone left low or if you find someone out of position(always thinking of the priorities of your targets first), patience is the key to a good Kha'Zix player, remember that you are an assassin and extremely squishy, one mistake can cost you your life. At this point of the game you start using a lot the "Late Game(level 16+) assassination attempt to invisibility"(see Combos chapter below), fast thinking and reflexes are your friends.
Tips & Tricks
Casual Lane Harassment: Auto Attack () +
Level 2 Lane Harassment: This requires you to be level 2 before your enemy laner does, once that's done you can level up (I recommend you are using a hotkey to level up at that time to be very fast) and jump on him when he is behind his caster minions to have him isolated while he is still level 1 giving you the advantage early on.
Level 6 All in: > > > > Auto Attack() > (second stack) > Auto Attack() OR if its up >
Late Game(level 16+) assassination attempt to invisibility: > > > > up to your judgement whether you will retreat or go in again.
Pick Kha'Zix when the enemy team has relatively squishy champs and not very hard cc champs, as an assassin you want to be able to move freely and kill your enemies fast.
Kha'Zix works best with an AOE team comp, because in a teamfight with an AOE team comp there is always gonna be someone with low hp after all the damage done.
Sure thing though dont pick him when you have another assassin like Talon, Zed or Akali on your team.