Sorry for my bad english. This kata build is for pro only and please dont complain if you fail with this build.
At first of all i want explain why i choose the runes. i prefer taking full ap and magic pen. why?

Because the Q spell makes a lot of damage without being near the enemie. in every game i rule in the mid because of skilling the Q as fast as possible to do more damage in range. The W-Spell is only needed one time because we prefer using the Q-Spell and if we skill E-Spell you can only hit one time. Calculating the damage, the Q-Spell makes a lot more damage. Now i try to explain why i use a full ap mag pen build. because of our Q we can stay at range and the enemy doesnt attack much. so we dont need def or something like that. Only ap.

TELEPORT?? WTF????
The only use for the teleport is getting fast to all lanes and killing with E-Spell and R. All people who say its a fail, have never tried teleport with kata. you can place wards on bot and port from mid to bot and kill all enemies. like a jungler ganks.

Flash of course because of flashing out of the fighting area.

Item Sequence.
The first item would be the shoes. Why? Speed is necessary for kata. Because we need to go near the enemy and throw the dagger. After this we need to run away. If the enemy got low hp we attack with E then W, Q and R, by the way. The hextech revolver is necessary to recover katas life. Every dagger would heal her.
Now i want to explain why i named this guide for pro only. After the revolver we buy meijas.
If you know how to play with kata you only die about 3-5 times and good player make about 15-25 kills a round.
Buying meijas in early game would help you to stack your meijas from beginning and becoming very strong in the early game to rule the whole game.
after this you need to buy your magic pen shoes. why? just because of making more damage. the cooldown reduction shoes are not necessary because of her low cd. 20 stacks on meijas got enough cooldown reduction for kata.
Then we need to buy the giants belt. Why? kata got low hp and very easy killed. so more hp helps you to stay alive in fights. Then we buy the hextech gunblade. very high damage and spell vampire and lifesteal and active. the next item would be rylai's. if your ulti hits the enemy, hes slowed down. and after this item you should kill a lot more people then before. then we buy rabandons. we dont need to explain this step :) Now the enemies would say. kata is so OP, lets buy magis res. now its your turn to buy magic penetration. the void staff is the best item to penetrate the enemies magic res. now i hope you understand why i use this sequence. if you have question please send it to me:)