If you're in champ select right now and you're playing Kha'zix for the first time, here's the short form:
Take 21/0/9 masteries. Flash+Ignite. Mecha Kha'zix skin (not optional). Start flask+ward+four health potions+one mana potion. W>Q>E, evolve W>E>R>Q. Go to the “AD” tab in the shop and buy anything that looks pretty. Done. Details are below.

So, you want to play Kha'zix. As with most subjects, it's important to be very specific. Where you want to play Kha'zix? Even more specifically, which lane on which map do you intend to play Kha'zix? While the overall ideas behind playing Kha'zix are similar across all maps and lanes, the differences are significant. For example, a jungle Kha'zix build on Summoner's Rift would be very different than a botlane Dominion Kha'zix build. I will try to address these concerns in the guide, but the reader should use discretion about the circumstances of their Kha'zix pick.

First, down to brass tacks. I'm not going to lie to you. Kha'zix's early game is awful. You know how champions like Garen, Riven, and Darius are known to bully weaker laners? Kha'zix is that weaker laner. If you take him top lane, you need to understand that champions like that will be stronger than him. In fact, it's highly likely that they will do their best to deny you many creep kills early in the game. This is largely unavoidable.

However, it is not the end of the world. Patience is of the utmost importance when playing an assassin such as Kha'zix. Your absolute main priority in the low levels is to survive your lane. Even mid lane, where you are up against squishy champions, they have more ranged harass than you do, and often have surprising damage with Ignite. Don't get baited into trying to go too aggressive early. Be patient.

If you're in a lane matchup like the ones described above, where the enemy champion is strong enough to beat you early game, don't panic. Because your focus is on farming and surviving the early game, you should focus on leveling up your W ability, Void Spike. Now, because you're a total baller and you're using the Mecha Kha'zix skin, your lame spikes will be replaced by totally sweet missiles. These are your primary harassment and farming ability; you will use them to pick up creep kills that are too risky to take in melee range, and you will use them to harass the enemy champion if you feel you can afford to do so. As you'll notice quickly, leveling this ability first gives it an absolutely massive mana cost. Because of that, you should pick up an early Crystalline Flask and potentially some supplementary mana potions. You won't regret it.

At level 6, you'll have a single level in Q, E, and R, with three levels in W. The order you take these is situational; if you expect jungle ganks, you should absolutely take E at level 2 rather than Q. If you think you can play aggressive, then Q may be wiser. Always, always take R at level 6. You now have the choice of evolving any of your three abilities. I feel that in almost every game, the ideal choice here is to evolve W. The reason for this is simple. Q is extremely cheap in mana and has a very short cooldown, but it puts you at risk of counterattack due to its short range. Almost every enemy laner can return more damage in a trade than Kha'zix (because they'll be too near their creeps for you to get the Isolated bonus damage). Evolving E is not of much use in lane, since it doesn't increase your damage and you won't get many cooldown resets from kills in lane. W, however, dramatically increases in harassment potential with the bonus damage from applying your passive, and the wide AoE is very useful for pushing the creep wave if needed.

Void Spike is Kha'zix's bread and butter. Ignore Phreak's spotlight, ignore the obvious “Q>W>E” logic. Leveling up Void Spike and evolving it first makes the most difficult lanes tolerable, and it turns Kha'zix into a monster midgame. At level 6, Kha'zix evolves W and becomes a proper assassin. I usually prefer to push the lane out at this point and try to gank an adjacent lane, but this is optional.

Many of the lane bullies start to have trouble with Kha'zix at this level, because sustained harass from fully-leveled Evolved Void Spikes really chip away at their health without giving them opportunity for counterharass. If they ever dive onto you, feel free to simply jump to safety and resume the Void Spike harass. As long as you have the mana for it (which a Flask and mana potions should guarantee), you can shove some surpisingly scary laners back to their tower or force them to recall. Naturally, if they fall low enough from the harass that you think you can kill them, go ahead and finish the job. Jump in, fire some rockets, Taste Their Fear, and ult if needed.

Don't forget to weave in autoattacks between abilities, and pop Ignite early if possible. I recommend against tower diving, because Kha'zix's squishiness and lack of hard crowd control makes the dive very risky. It's much easier to simply chase them out of lane, push to their tower, and then gank another lane. If you're top, gank mid, and if you're mid, gank bottom. If you start to pick up kills, then your team can probably take Dragon. The enemy will probably attempt to put pressure on top lane tower when you do that, but if you see that it means the Dragon should be safe and you can take it without the threat of a lost fight.

At this point, the midgame has begun in earnest. Lanes will become more fluid as towers fall, roaming becomes a major activity, and ward coverage becomes absolutely vital. Do not be the weak link that does not buy and place wards. At level 9, Kha'zix is quite scary. Void Spike is maxed, evolved, and Taste Their Fear should have two ranks. His rockets (with his passive up) will be doing significant damage from long range, and applying slows on stragglers that the team can follow up on. Not long after, you'll hit level 11.

Here is a major choice point. Evolving Q, E, or R. If you find that you are fed or that the enemy team is composed primarily of soft, squishy targets who are easy to assassinate, your strongest choice is to evolve E. The increased Leap range is very significant for jumping to those squishies, and more importantly after you take one out the cooldown will reset, letting you more easily reach the next. Keep in mind your mana costs; try to always remember to pop a Flask or mana potion during the fight so you don't end up out of mana and missing a kill.

If you find that you are not usually being killed quickly in fights and the enemy team is not easy to assassinate (for example a team with champions like Singed, Malphite, and Swain), then evolving Q will help cut through their significant health pools. Finally, if the enemy team is coordinated enough or just bursty enough that you expect to be killed quickly in fights, evolving R is almost mandatory, if not now then at level 16. The extra stealth time and decreased damage during stealth is very very powerful for keeping you alive.

Finally, keep in mind that you are playing Kha'zix, not Fiora. You have options beyond “dive in and hope you can kill them before they kill you”. Jumping into an enemy and trying to kill them should be saved for after they've been harassed down to low health with Void Spikes. It's safe, reliable, and the slow allows you to control the terms of engagement. As the game goes on, you must play even safer, because the grouped teamfights characteristic of lategame are not kind to an assassin whose primary defense is negated by Oracle's Elixir.

Now, for item builds, Kha'zix is actually more versatile than many realize. While the high-damage assassin build is very strong on him, there are situations in which defensive options are more important. A Brutalizer, and by extension the Black Cleaver, are very good first items, and are almost never a bad choice. After that, however, the options are many. If damage is your only goal, a Bloodthirster or a Last Whisper (for low and high armor targets, respectively) will allow you to cut through almost any defenses, while slightly tankier damage items such as Hexdrinker, Phage, or even Frozen Mallet are safe choices.

Finally, after you feel like you do enough damage, it is usually a smart choice to build purely defensive items, such as Guardian Angel, Randuin's Omen, Frozen Heart, or Spirit Visage. Cooldown Reduction is an excellent statistic to pick up from defensive items, find it where you can.

As for boots, Mercury's Treads are (as always) an ideal choice against teams with dangerous crowd control, Ninja Tabi lower the threat of AD carries, and mobility boots vie with Ionian Boots of Lucidity for aggressive options.

Note that Sheen is a largely wasted purchase on Kha'zix, because his burst should happen before you would even get a chance for a second Sheen proc. Keep Sheen on sustained-damage bruisers, Kha'zix has better choices.

If jungling, the above guide is still absolutely viable, just remember to start out with a Machete and upgrade it into a Spirit Stone early for the safer jungle clear. I would personally not upgrade it further than that, and return to a normal assassin build afterward.

Good luck out there, and make me proud.

What do you think of this guide? Let me know in the comments. Did you like the in-depth text-dump style of guide, or would you prefer a more terse, bullet-pointed guide with more pictures? The only way to get the sort of guide you want is to ask for it.