Katarina, though she might be said to be a brainless champ, however she isn't. She uses a fast combo and requires fast thinking and mouse precision.
Her early game isn't bad, for level 1 and 2 against ranged champions however as soon as she hits level 3 she can do a full combo and an ignite to get a kill. You are going to be using your Q to poke enemies from far away. Your E will be a way of escape, if you press E on a friendly champion or any monster/minion you can blink on it, this also works for plants in the jungle. When you E and there is a dagger under the enemy, E onto the enemy to get the E damage and then you will pick up the dagger, thus getting a reset and dagger damage on the target. Your W will drop a dagger to the ground on your current position. If you believe that someone is going to gank you, or if you are taking turret, drop a dagger so you can E onto it and escape. Her ult cooldown drops after she gets a kill and if you E onto a target, use W and then ult, you will deal the most damage, and afterwards add a Q if they aren't dead.