So guys. This is my first build/guide. I dont have much time on my hands right now, so im gonna make it short and sweet. I thought I should contribute to the site seeing as ive used it for so long :) Try not to be too harsh!

The runes and masteries should speak for themselves cause Kats skills used AP and AD.. The Ability power and Attack damage runes are what I used.. I dont have a full set of the cooldowns but thats what I would have.

Pros

High Damage
Farmer
Late game ownage
Easy Farming
Great skill combos

Cons

Low HP till mid game
Pretty squishy
Stuns are the bane of Kat
Gankers WILL kill you
Expensive build

I always mid with Kat, if my team hasn't shotgunned it first. I take the boots and 3 health pots. This is to keep me in the lane longer than my opponent. Then I slowly build up to the hextech gun blade.. I know it takes time but you should be alright for kills if you go mid.. You just gotta get you team to call mia's all the time cause your health is gonna be real low for a while. I go for the Hextech revolver first then build up from there, grab your upgraded boots whenever you can.
Once you have 2 Hextech gunblades you should be reeling in the kills really easy. You may have a few deaths so your gonna need health.. I go for the Crystal Scepter for the health and the slows when you use abilities. The AP on to is just icing on the cake.
After this build up for the void staff.. the AP is large and the magic pen is amazing for kat.
The last item I go for depends on who your against.. If your going for high damage players.. Panth/Yi etc. Then I usually go for the hourglass.
If your just owning them in general then I go for the Deathcap cause it will own anything you go against.
Finally if your against Ryze or someone alike then I go for the banshee viel. Self explanitory.

The skill sequence im not 100% on.. I always start with Shunpo and then your killer instincts. Obviously grab your ult whenever you can. and Dagger for farming the minions. Once you have your 2 Hextech gunblades your spell vamp is immense with the killer instinct/throwing knife combo.. you'll get pretty much all your health back.

Early game I usually own weaker champs in the mid. Hit your killer instinct, and shunpo on them.. you'll receive damage reduction from killer instinct and shunpo is a pretty hefty move. If your running low on health after shunpo'ing onto them hit your heal spell to regain health.. You will usually need to do this if they are high damage.. Squisher champs, Ashe/Teemo.. you wont need so much.

DONT REFER TO THE ABOVE SKILL SEQUENCE. ITS NOT CORRECT.

So there it is... Hope it helps, like I said first guide.. and I have no idea how to code or anything Il try get a screenshot up of some scores or something if i find how.. Thanks. Let me know what you think. Also feedback to help me improve.