Not Updated For Current Season
Alright here is my style of playing Katarina.
Best case scenario, you are in a solo lane. Best case scenario you have stuns on your team.
So what you want to do is play pretty defensive at start. Just harass with bouncing blade on who you are against. Morde sucks. So when you get your ulti and the enemys health is pretty low, wait for an opportune moment and Shunpo behind a creep behind them then ulti. The reason why we Shunpo the mob behind them is their initial reaction would be to walk back to their tower, which is going to be through your ulti. From there you just go from lane to lane ganking with your team with snares/and or stuns. The guardian angel is to protect your stacks. When I play kat I play super defensive so I do not lose stacks. Once you get 20 stacks you pretty much GG the game. End game you can switch brutalizer with bloodthirster.
Good luch hope this helps!