Sometimes you can waste a lot of Poke balls on just one Pokemon that you just can’t catch. My tip is that if you’re struggling to catch a Pokemon (or if you just want to make catching Pokemon generally easier), try turning off the Augmented Reality setting (It’s in the top right when trying to catch a Pokemon, it’s called “AR”).
It makes catching them less funny, but it sure is easier.
I’ve just read that the best time to throw the Powerball is when the green ring on the Pokemon is smallest. Hold the poke ball down until the green ring is small, then swipe with your finger to catch it.