erlernen: mostly refers to a profession. e.g. Er erlernt den Beruf des Bäckers. - He is being trained to be a baker. ausüben: also refers to work, but once you've already learned how to do it. e.g. Er übt jetzt den Beruf des Bäckers aus. - He is now working as a baker. üben: could be anything you practice (instrument, languages, mathematics,...). e.g. Üb deine Englischvokabeln für den Test morgen! - Practice your English vocab for the quiz tomorrow!