1) Always land a Q and try to move in without using E. Saving it for an escape will max your kill potential, because you will have to win a few small trades this way to have enough damage to get a kill.

2) Use ult two force other mages out of their combo. Examples like le blanc diving in for damage, then you use ult to get her away and poke her with Q on the way out. Then you can shunpo back to her, and W to finish her off. Let champs come to you.

3) Try to auto attack minions that your minions aren't hitting and lower down a group of 3 or 4 so you can clean them up and get 4 cs at once with a Q.

1) Keeping your distance early in the team fight is kat's best strategy. You are the all in dive finisher. You can turn a teamfight that looks grim into an even trade or even an ace with your ultimate, but it wont work if you go in too early.

2) Make sure some major cooldowns get blown BEFORE you ult. For example, look for a Zhonya's to have already been used, or other champion ultimate abilities. This will insure when you shunpo into the action and hit a magical R and spin to win, that they can't kill you before you have dealt maximum damage.

3) Use smart Q's to get to the back line and poke the carries. It's kat's only ranged ability so make sure if you do get some damage in early, it hits the guys that count, like the enemy's ranged carry or mid laner.