So who am I?
Well I am Katarina OTP that has played over 350 ranked games with her this season. I post highlights on my YouTube that showcases why Katarina is such a great and fun champion to play.

The Guide
In this guide I will try to explain why and how to play Katarina effectively, providing insight on the best pre-game set-ups, builds and play style. The guide will be continually updated and changed as each patch can affect her build or play style. If the guide has helped you consider liking the guide and visiting my YouTube Channel. Any feedback on the guide is appreciated, your discussion and insights can help other players so get involved.
Thank You,
JustShiney

No matter what electrocute is a must on Katarina, it helps her have insane bust and the rune tree is strong. Sudden Impact procs off your Shunpo to give you extra magic penetration.Eyeball collector is then the second option as this again increases your damage, alternatively go for zombie ward for more safety in lane. Finally go for Ravenous Hunter for life steal during team fights. The second tier of runes is up to you. Precision, Resolve and Sorcery are all viable. Certain match-ups such as Zed or Yassuo may require resolve to survive their all ins. Go Bone Plating and Chrysalis in these instances.

Pros

Great snowball potential
Can 1v1 most mid laners
One shot squishy champs
Great roams
No mana
Resets mean huge multikill potential

Cons

Can be knocked out of ult by most cc
Can struggle if behind
Squishy
Need to kill with combo or you die
Poor against tanks

The skill sequence for Katarina should always start:
Q>E>W
After this you have your basic combo that can be used to kill most champions at around half health.
From there you can either continue to max your Q first and then E or can put another point in E to reduce the cool-down and make the basic combo easier to hit (landing on your daggers in range of enemies).