Jeff Tucker from GSX Athletics presents his muscle-up training progression. Jeff is the coach for the CrossFit Gymnastics certification seminar.
The first step is to have competency in a stable environment, such as with a bar dip. Then you should be able to hold a stable support on the rings. Next is the ring dip. Only when this can be performed comfortably should the rest of the muscle-up progression begin.
The false grip is essential, and the elbows must be kept in tight. Then, the transition can be practiced on the toes. This develops the strength and muscular patterning required for a stable and consistent muscle-up. Within a few months of simple drills like this, raising the rings a few inches at a time, the full muscle-up will come.