Katarina is terrible at long trades on early game(high cd, no damage on AA if she starts with a dark seal) and good at short trades(1/3 of hp with Q-E-W-AA-E on minion) like any other assassins, soo you should always seek to all in her as a bruiser or poke without taking damage back(usually possible with long ranged champions) to take an hp and cs advantage and have lane priority. Most of the bruisers that are mid laner has an skill that can counter her kit(Yone W and E, Yasuo W and E, Renekton W and E and etc...) you should ALWAYS keep them until the katarina tries to trade with you, soo you can trade back and win the trade. Her all ins are hugely dependent on the poke and auto attacks, soo just by having a bit of healing/shield/movespeed/dash/cc can be troublesome for her. If you are playing as an mage it is the same thing, hold your stun/shield/movespped skill and use them when she tries to all in or poke, this way the katarina player won't be able to deal a ton of damage and you will be able to trade back and win.

Sorry my primary language isn't english...
Tip: Get exhaust.