Succeeding on Kai'Sa 101
I have seen people do the wrong thing with Kai'Sa and building the wrong way, so I will help with a very basic guide with her.
_________________________Step One: Your focus is NOT a typical critical striking build, it is going down the Rageblade path, I will give more details on this.
_________________________Step Two: You can dash backwards with your ultimate and it gives a massive shield. This is a HUGE steroid for a marksman to have for kiting purposes and straight up defenses purposes with that shield. DO NOT dash in to start a fight, you are NOT Vayne, you are NOT an assassin, you are an extremely power hyper marksman - this means your early-mid game is on the weaker side until you get your items / build rolling to really take over the game.
_________________________Step Three: You want 100% bonus attack speed as soon as possible. Not only does your passive scale with attack speed / ability power (this second part is important, get to that in a bit), but once you reach 100% bonus attack speed you unlock your invisibility for 0.5 second which is another massive defensive steroid in teamfights since it de-aggros the enemy team's attention away from you, which is what you want as a squishy marksman.
_________________________Step Four: Guinsoo's Rageblade and Hextech Gunblade gives you enough ability power to upgrade your W, core items to get because of that, and because you have really high ability power ratios on everything. To compliment this you build Runaan's Hurricane since your passive is on-hit and your cooldown reduction on E is on-hit as well, so when Rageblade and Hurricane are working together you always have your E up and you are passive proc'ing everyone! Your invisibility is the more important upgrade to get, doubling Q missiles is nice and W is nice for the poke damage (which it does 50% increased damage when upgraded, but the tooltip does not say this for some reason).
_________________________~ Essence Reaver is a good item to get later in the game for the 30% CDR, allows for more Qs and even more Es. _________________________~ Wit's End or a second Zeal item are both good, Wit's End great for the magic resistance and MR shredding, also more on-hit damage with Hurricane/Rageblade is always good. (Just a couple of additional options, but your core trinity of items is Rageblade, Gunblade, Hurricane in no specific order, rushing Gunblade does give a nice early game spike when you have it, but you do really feel the lack of attack speed when you do this.)
_________________________Step Five: Last Whisper and Void Staff items are both pretty useless. Your damage is very mixed so do not buy either of these items because they are only half effective on Kai'Sa, this is actually a benefit hybrid champions like Kai'Sa has because you can afford to get a completely different item instead to pump out even more juice (or a defensive item if you really need it).
_________________________Step Six: Remember that your W has long range and provides vision around it, so use it to scout out an area and stay safe. You are a pretty immobile marksman so utility like this is very strong on you.
_________________________Step Seven: Just want to re-emphasize that you are NOT an assassin or Vayne, you are a hyper marksman strong in the teamfights and when your team enables you to do well / does not abandon you to let you die to the enemy team. When you pick Kai'Sa you are actually picking a very damage heavy marksman, you are pretty immobile and shorter range, but your invisibility and shield are more than enough to make up for that in the late game to keep you alive.
DO NOT DASH IN AS KAI'SA!!! The only time you EVER dash in as Kai'Sa is when you are for sure safe, a teammate is nearby to help you out, or you need to dash in to help out a teammate/teamfight that is far away. Your ultimate is best used for dashing away from your closest target to kite them and making use of the massive shield it provides to stay alive and completely massacre the enemy team.
Kai'Sa is a pretty advanced marksman to play as despite her kit looking pretty basic to use. There is a lot of on-the-fly decision making and thought process that needs to take place, both in in-combat gameplay and how you build / what order you build your items in since Rageblade, Gunblade, and Hurricane all over different things based on the situation that you need them for - you eventually will have all three of these items, but that takes time and gold.
Hope you find this helpful and have a nice day everyone! [sg-kiko]