The basic idea is that when you push a button it needs to increase the Z of the entity. To practice just have it move the charter's Z position while the key is pressed. Use no Gravity in this experiment. Then have it decrease the Z as gravity normally would an use collision detection.

While I've not looked at AUM 79 one problem you might have is that your character could be so big that the bit that is jumping by could nothing for that size. Try increasing the amount you jump by.