This is an in-depth guide for the newly added champion to the PBE server, this guide has not yet been tested on live servers since the champion has not yet been released on the live servers. Be advised , the guide is probably going to change as the champion gets released and balanced, keep a close eye on it for the latest updates.

Now as for me,I've climbed the ladder for 25 days and I aim to reach at least Diamond rank this season and start streaming. I'm currently a Gold 2 player, I've been placed in Silver 4 this season due to some really rough placement games. I've peaked at Platinum rank but due to the MMR decay for inactivity , I've been demoted at that time into Gold.

Note: Kai'sa's abilities scale with Attack Damage, Ability Power and Attack Speed. Q and W scale with both AP and AD , while your E scales with Attack Speed. The shield we get from R also scales with both AP and AD.
SECOND SKIN(Passive): This passive acts like Vayne's passive but instead of 3 stacks you need 4 + another basic attack to proc it, this also can be used with Runaan's at the moment to apply stacks on the entire enemy team. This passive scales with AP and it deals burst magic damage. Also, allies using immobilizing effects also apply a stack of your passive on the enemy.

ICATHIAN RAIN(Q)is your wave clear.This ability however is a bit tricky, it has several missiles that each have a mind of their own, literally, to maximize the damage you need to have the enemy champion you're focusing be isolated , this works like kha'zix's isolation damage, however if there are multiple targets this is going to target everything in range of the 6 missiles, so if you have a minion wave this is going to probably hit 4-5 minions and 1-2 enemies. We can't rely on this ability for champion damage ,however, the AOE clear after a couple of AD or AP items is really good. This ability can be upgraded at +100 bonus AD bought. The upgrade gives you massive damage on your Q and fires 12 missiles instead of 6.
VOID SEEKER(W)is your biggest source of damage as it can not only pop the passive but it can also apply 2 stacks of it if needed.This has a super long range and it can be used easily in combination with your ultimate Killer Instict(R). This ability can be upgraded at +100 AP bought.
SUPERCHARGER(E)This ability makes you unable to use any of your other abilities or attacks for the duration , it gives you movement speed and after charging a boost to your attack speed. This should mostly be used for positioning or escaping as it is really bad in a fight since you can't use anything while supercharging. This ability can be upgraded at +100% attack speed bought. The upgrade gives you stealth and the attack speed you buy decreases the duration of the supercharging effect.
KILLER INSTINCT(R)is basically a dash+shield but you're forced into applying a stack of your passive on an enemy champion to even be able to use it so this is mostly good if you either fight already or have someone immobilize the enemy so that your passive is applied on them.The shield scales with AP so this can get pretty huge, we're talking about numbers like 900+ shield HP.

Note: Ability maxing order remains the same in all roles, Q first then W and E last.
Note 2: Icathian Rain can and should be used for securing minion kills (CS) in difficult matchups like Caitlynn ,Draven, Tristana.

As you all can see, we have a lot of good rune choices for Kai'Sa due to recent rune changes and additions.
Hail of Blades is one of the better "hidden" runes if you will... it has extremely good synergy with your passive and Guinsoo's Rageblade. It gives you 3 extremely fast auto attacks which allow you to stack your passive Second Skin and Guinsoo's Rageblade's item passive. Note: This rune does have a cooldown however and you need to go in and out of fights often after the first 3 hits have been done.
Sudden Impact Gives us both lethality and magic penetration and this works because of the stealth mechanic which comes with our Superchargeability.
Eyeball Collection gives us AD on ward takedown up to a maximum which is pretty good in my opinion.
Ultimate Hunter will allow us to get our ultimate ability Killer Instinct faster and use it more often as it gives us cooldown reduction on this ability specifically per 5 unique champion takedowns.
Celerity, now this has been touched recently by Riot and the movement speed has been reduced to 1% but the AD/AP increase from flat movement speed has been greatly increased so it has it's uses giving us some more damage.
Gathering Storm, this rune is for lategame as it increases our damage even further as times goes by, in this game it gives us some massive AP and since Kai'Sa scales extremely well with AP it fits perfectly in her kit.
Phase Rush this gives us movement speed per 3 hits on the same champion and can easily be stacked and it also has great synergy with Celerity due to how both runes work with movement speed.
Second Wind, this is a good rune if you want to survive more in laning phase, against high poke lanes this might just be your saviour.
Ravenous Hunter this is also good for sustain as it gives us a stacking lifesteal bonus on our abilities after some unique champion takedowns.

Fleet Footwork and Overheal work really well together to balance out the healing we need since our auto attack range is pretty low compared to champions like Caitlyn.

Press the Attack this adds some damage to the table but you reduce your attack speed greatly by not having either Hail of Blades or Lethal Tempo so take this if you just want to burst someone down fast since the damage it gives us kind of nice.
Nullifying Orb great for current meta as we have a lot of champions like Swain and Fiddlesticks in the bottom role.

Legend: Alacrity gives us a stacking attack speed bonus on champion takedowns.
Coup de Grace gives us a good damage boost on low HP targets which is great for every ADC.

Lethal Tempo more attack speed for more passive procs; note: this has a lower attack speed boost than Hail of Blades and I'd say take this only when you know you'll be fighting a lot and not be going in and out of fights.
Triumph gives us some gold after champion takedowns which allow us to get our items faster so you might want this in some cases.
Bone Plating works really well against the current meta where we even see champions like LeBlanc in the bottom role lately.

Conqueror this is tricky to use but it adds a lot of true damage to the table if you are able to stack it up and use it to its true potential.

Kai'sa is a highly mobile champion hence why she can be played in multiple roles. She's basically the Akali of ADC's.
She not only has high burst damage but also sustained damage due to her high attack speed and high cooldown reduction granted by this build. The DPS(damage per second) she brings can be massive if used correctly. She also uses her ultimate to dash in and shield herself , this can be used to secure kills and should almost never be used to dash into a teamfight inside the enemy team, unless you have a lot of AP which boosts your ultimate's Shield HP or unless you have the enemy team distracted so they don't focus you down as soon as you get there.
Managing your Passive plasma stacks is crucial for your damage output to be high. Your attack combination until you get enough attack speed or AP to easily apply plasma procs is AA+Q+AA+W(2 stacks non upgraded it gives 3 when upgraded)+AA , this combination ensures high damage output and the 5 needed attacks to proc the 4 stacks of plasma from your passive.
You have a lot of gank potential since your passive can be applied by your allies and you can jump with your ultimate on your target that has the passive applied to them. You can also easily roam due to the movement speed you get from your E.

Overall Kai'sa's a better Vayne with higher mobility, higher burst damage and a big shield on top of it. Her team fighting phase can be extremely strong if her abilities are used correctly. To get the most damage on a single target in a teamfight try to stay on the outskirts of the fight at maximum Icathian Rain range so that you only hit 1 target and apply maximum Black Cleaver stacks on only 1 person but note that Black Cleaver can easily be stacked on the entire enemy team as this build adds a lot of cooldown reduction and Icathian Rain adds 1 Black Cleaver stack per missile,meaning a total of 6 stacks per 6 missiles without the upgrade on this ability. More explaining on this part is done in the Item Build Chapter of the guide, down below.

For summoner spells we have Heal which helps us with our HP problems during fights and allows us to survive more, Teleport which can prove useful in some situations and allow us to pull ahead in CS , Cleanse which can save us from CC and allow us to escape and Barrier which can block some burst damage and allow us to live a little longer. For jungle Smite is the obvious choice as it's needed.

We're taking Doran's Shield as our first purchase as it helps us in lane phase.
The addition of the Spellbinder instantly upgrades Void Seeker as it adds +100 Ability power ,it also adds +10% movement speed and an extremely good stacking bonus of AP and movement speed per spell cast that can go up to +100AP and +30% movement speed for 4 seconds. Since we're an assassin type marksman which scales with AP as well , this items is extremely good for us as it instantly makes us stronger since almost all of our abilities scale really well with AP. Spellbinder also synergises really well with Kai'Sa's passive Second Skin as it's damage scales with AP and does a lot of burst damage. In some cases you might want to go for a more defensive setup and Guardian Angel or Death's Dance fit the role nicely in place of Spellbinder , consider this over upgrading Void Seeker if you feel your damage is enough and you don't need the extra passive stack it adds.

These Items are generally the same for all roles since the gold cost and efficiency of the items is the best, the build for ADC is exactly the same as the one for top lane and late jungle build as I found these to be the most cost-efficient items on Kai'Sa.
The build for mid lane I have here is an example of an unrealistic build as it requires a large amount of gold and can almost never be done in a high elo game.

Consider adding Black Cleaver for late game if the enemy team is more tank heavy , as in 2-3 heavy tanks like Malphite+ Sejuani.Take into consideration the fact that Black Cleaver passive is being applied by every Icathian Rain missile so you can basically fully stack Black Cleaver in a 1v1 situation. Upgraded Icathian Rain + Black Cleaver is an extremely powerful combination as not only does it add 6 Black Cleaver stacks per 6 missiles but you have 6 more missiles to spare as the upgrade hits with 12 instead of 6. This makes for an extremely strong teamfight presence as you easily hit multiple targets and apply the armor reduction on the entire enemy team.

Another thing to note is that Runaan's Hurricane does apply Second Skinstacks to all targets hit so in some cases you might want to add it as it might add more damage, consider this if the enemy team is more tank heavy.
You might not oneshot with these but you're going to be useful in all situations.

Guinsoo's Rageblade due to the recent nerfs is now primarily used on Kai'Sa for stacking her passive, the damage increase it gives us extremely low but due to how Second Skin works it is still viable and works really well with Hail of Blades.

For the Conqueror build there are some things I'd like to say, first of all, you need to be in combat for a long time to be able to use the rune so if you have no minions to activate it on then you're pretty much done unless you really know what you're doing.
Berserker's Greaves are not needed with these builds since we can use items like Spellbinder if we really need more movement speed but we have other choices like Ninja Tabi against heavy AD compositions and Mercury's Treads against heavy AP or CC compositions which can prove useful. Mercurial Scimitar and Guardian Angel as we're going to be in the middle of the fight when using our ultimate Killer Instinct work pretty well. Trinity Force is for a more damage heavy build against low armor teams, this item is here to replace Black Cleaver in this situation. Phantom Dancer can and should be replacing boots if needed for an ultra late-game build if more damage is needed and the enemy team has more than 1-2 priority targets on your team to focus on such as a Zed or Talon or even an Akali. Adaptive Helm is just a generally good item if you want more resistances against AP champions like Brand, Malzahar or even Teemo since Liandry's Torment is now a broken godlike item due to recent buffs.
Nashor's Tooth is a great item on Kai'Sa as it synergizes well with her kit, providing both attack speed and AP as well as magic damage on hit and a big chunk of CDR that works well with everything our kit has.
Rabadon's Deathcap is the cherry as it adds extremely high amounts of damage to the table and boosts our AP.
Essence Reaver is one of the best items you can buy as a first due to the synergy with killer instict, it gives a lot of flat AD and a lot of attack speed and cooldown reduction after your ultimate has been used.
Banshee's Veil is great for surviving and also gives us a lot of damage in the process.

This is the section destined for update notes as this guide is probably going to change as the champion gets balanced and tweaked on live servers. Keep a close eye for the latest news.
Update 1 (3/8/2018)
- Added more items to the build
- Added more of everything , literally
- Guinsoo's Rageblade status is unknown yet, this item is about to hit some major changes, it remains to be seen in patch 8.6 if we want it as a late-game item in our build to replace Spellbinder
- Precision+Sorcery alternate rune setup tested and updated within the guide
Update 2 (3/23/2018)
- Guinsoo's Rageblade status has been revealed, added to guide
- Precision + Inspiration with Conqueror alternate rune setup tested and updated within the guide
- updated build for Conqueror
- added Nashor's Tooth to situational items

Update 3 (7/7/2018) Patch 8.13
- Guide updated with everything that has been added recently