Just try to get Last-hits in your early game for farming,you can use your Sinister Steel (W) or your Bouncing Blades (Q) to get multiple Last-hits at once. Remember that Katarina's ultimate Death Lotus (R) has a very low cooldown. Because of this, don't hesitate to use it simply to deal a bit of extra damage in an exchange, even if it won't kill. In a teamfight, Katarina's most important decision is exactly when to initiate. When you initiate to teamfight use your AoE abilities to help your team and get kills.