Calisthenics Unity

I just started this program and how do I know when I need to move on to the next level.

when you do every exercise correct and for how many times he tell you to do it and do it as many minutes he tells you to do each exercise for

You can move to a next level when you do the minimum sets & reps but it's always good to push yourself to the maximum sets & reps you can do. You don't have to go immediately to the next level, sometimes I repeat the level 2-3 times, sometimes I go to the next level after finishing 1 time. And yes like Elias said, make sure you do the exercise with correct form and don't care about the reps but care about feeling the muscles being worked, don't just do the rep for a number but make sure you feel the rep, doing 20 kip pull ups is different than doing 5 strict pull ups.