Katarina is the most vulnerable when she has her on Cooldown (14 CD rank 1) and with reset (3 CD rank 1), which enables you to trade with her before she can close the gap.
Her main damage comes from activating her passive “Daggers”, so try to avoid standing close to these. Furthermore, try to keep at least 3 minions between you and Katarina, so her can’t bounce off to you.
Don’t blindly follow Katarina’s roams or you might get ambushed (unless you are stronger than her). Punish her by pushing the wave into her turret whenever she leaves her lane.
She has a very high damage output but at the cost of restraining her mobility in team fights and preventing her from resetting her . Use this to your advantage by taking her down when she is channelling her .
Prevent fighting in place of confinements like Dragon / Baron pit where Katarina can dish out damage to multiple champions in a short amount of time. As soon as she appears try, to lock her down or back away.
Katarina is not only countered by hard CC, but also by the general tankiness of your team. This results in less resets of her abilities through kills and assists and thus less damage during team fights. If you’re squishy- invest in defensive items.
Katarina’s major power spike comes with finishing Hextech Gunblade- giving her more sustain and more burst damage. Upon finishing Hextech Gunblade Katarina will force more trades. Don’t underestimate her healing abilities.
When the game transitions into mid game and your team starts grouping around objectives- where Katarina can kill your backline., try to keep your ADC covered and keep track of Katarina with vision.
Keep note of Katarina’s Zhonyas. As soon as it's ready she will try to engage the team fights and rely on the Zhonyas active for her team to follow up. She can force hard crowd control to be wasted this way and win the team fight.