So, that takes care of yaw control. Now, how does a multicopter move up and down? Here, it's similar to a traditional helicopter. A simple increase in the throttle of all the motors together pushes more air down. By pushing air down, the multicopter rises because the volume of the air flowing down from the rotors has greater thrust than the multicopter's weight. Decrease the speed of the propellers, and the thrust may stay the same as the multicopter's weight (providing a hover) or may dip down below the weight of the multicopter, causing a descent. The following image shows a good example of a multicopter holding a hover:
