Use Q to place the dagger behind the target and decide which side of them the trade happens on, then stay long enough to cash the free autos that setup creates instead of treating every touch as a dash-out combo
In fights, track the spell that actually stops Katarina before you track the carry; E and R get much better once the bind, stun, knockback, or point-and-click interrupt is already gone
Katarina side lanes best as a short show-and-disappear threat, and when she falls behind she usually gets back into the game by making the map messy enough for reset chains again rather than sitting in a long announced side lane
Ult when the fight has already committed enough that the obvious interrupt is gone or pointed somewhere else. In lane, that usually means after you forced the stun, bind, knockback, or panic movement with dagger pressure and E, not as your first statement. In skirmishes, look for the moment a target is already stuck in dagger space, slowed by pathing, or busy hitting someone else. If you have to ask whether they can still cancel it, wait a beat. Katarina gets much more from a slightly later R that sticks than from an early one that gets clipped and leaves you with no reset path.
Whenever an enemy champion dies that Katarina has damaged recently, her remaining ability cooldowns are dramatically reduced.If Katarina picks up a Dagger, she uses it to slash through all nearby enemies, dealing magic damage.
Katarina throws a Dagger at the target that then bounces to nearby enemies before ricocheting onto the ground.
Katarina gains a burst of Move Speed, tossing a Dagger into the air directly above herself.
Katarina blinks to the target, striking it if its an enemy, or striking the nearest enemy otherwise.
Katarina becomes a flurry of blades, dealing massive magic damage while she channels to the 3 nearest enemy champions.