How do I play the new Katarina?

seems entirely alien to me compared to before the rework, other than her Q and her Ult. You can judge my first time playing her on blind pick. Now there's this mechanic where you teleport to daggers, which makes you use the old W (which does more damage than before), but also makes it seem extremely difficult to engage/disengage. I'm just going to assume I need to re-learn Kata. Soooooooooooooo..... any guide on how to play the new Katarina? What are the basics on engaging/disengaging? How do I use my abilities correctly? Any specific combo?