If you are a top laner, invest in Magic Resist even before Katarina gets fed. If you jungling, keep an eye on mid. If she wanders, don't leave it up to your mid to call MIA. If you can, and it's not out of your way, try to intercept her when she goes to gank top or bot. If circumstances permit, by all means gank for mid and try to set her behind, by getting your min laner ahead If they are killed once or twice, try to tip the balance back in your mid's favor. If you can't do that, focus on stopping Kat from snowballing off top or bot kills. Since that's where she goes when your mid dies, to get more kills in a short period of time off resets.
If you are support, whenever you can, roam up to mid , sweep for wards in the river bush, plant a ward of your own, and if you're the kind of support with the kit that allows it, gank for mid and get a kill or burn a summoner's from Kat. If you are ADC, make sure you return to lane with a the very least a Green ward every time. Plant either your tri bush or the river bush, and don't let Katarina roam to kill you. Just back up and make her waste her time and miss out on cs without a kill. If team fights, do what an ADC does, position, hit who ever you can whenever you can with the least risk to you, tank or not. If you can hit someone, do it. If it doesn't get you killed. Pay attention to where Kat is while simutaneously hitting who you can.
When she Shunpo and Ults, make sure you aren't caught in it, or make sure you quickly get out of its range. If your team applied a CC, or when Lotus finishes, that's when you try to light her up and punish her even if she gets away. As the mid laner your role is to deny Katarina farm, harass her when she tries to CS/when you can, and out trade with her. I've honestly counter picked a Sivir into kat mid before and performed very well. (Yes we won, didn't stop, but slow secured victory) I spell sheilded every bouncing dagger she sent to me, leaving her with less incentive to pursue a further trade against me. She didn't feed me, but also ..... didn't do much. I however did pretty good without an insane carry KDA.
It's not so much about killing Kat as it is about making her irrelevant and useless. Make sure you ward both of the river bushes as a mid. Don't let her jungler catch you and set her snowballing. If you can stop Kat from becoming a monster you will never have to deal with her as one, and when she's become one there is at least a poot's chance in graceland to fix the mistake.