katarina is a very durable champ in mid with a powerful early game harass and an destructive mid game clean up and kill combo, this build focuses on pur attack damage and the ability the slaughter champ after champ...

the rune set up for katarina can be changed constantly depending on how you feel the champ needs to be altered due to your team or how you wish to play.

I found that the best set up is to focus on high runes of magic penetration, health and health regen. this gives you the ability the only build your AP into the game as your health will be scaling well, i sometimes build some resistance to the enemy team late game depending on how it is going..

The ideal mastery set up for katarina in my mind is 21-9-0 as this means early game is already set with a decent AP and health. AP is the most important thing with building katarina,

I always start with the basic
Boots
3 health pots
ward

This allows kata to get in lots of early feed and this make a treat for the enemy late game.

My favourite items to consistently build with Kata are:-
Blasting wand
Amplifying Tome
Haunting Guise

The first 2 items on the list allow you to repeatedly build into things such as rabadons deathcap, void staffs, abyssal spectre...repeating these 3 items can serve you very well as your enemies health will drop. The Haunting Guise allows you to build into the one of my favourite items usable for her...Lindry's Torment, this item will massively increase your CS with the burning of minions and the extra harass on enemy champions as they are ignited.

To start i usually get all of my abilities and then max my E and when necessary my W, this dive and then spin allows a harras on champs and then a quick getaway with the movement speed. I begin to build my Q later game as it only serves as feeding and a small damage. As normal level up your ult whenever you can.

I usually have flash and ignite on kata as it allows a escape, gap closer into your E, and a finisher if the champ is escaping.

The way to gain feed with kata is a combination of her Q and her W as it deals damage to many minions and a potential champ. Into the game you can use the combo of slowly eating their help with the Q and then a E,W combo to eat their health...If the champ is on low health dont be afraid to repeatedly use your ult and abilities as your passive with help you regain these in no time.

Katarina's most threatening opportunity is how she can clean up in team fights or ganks...with A Q,E,W,R combo you have the potential to kill a whole enemy team with up to half help, having help from a crowd slow or leap is very helpful here.

Thanks for reading hope this helps...