A muscle-up is a pull-up followed by a dip. It is usually done from rings, although it can be done from a bar. The muscle-up has been described as the hardest pull-up you’ll ever do followed by the hardest dip you’ll ever do.
Two keys to the muscle-up are the false grip and the transition from the pull-up to the dip. The false grip positions the ring far back on the hand, as close to the wrist as possible instead of in the fingers. The primary concern of the transition is getting the body forward through the rings so the elbows will come up over the hands into the bottom of a dip.
The CrossFit Journal has a great article describing the muscle-up.
Muscle-ups can be scaled in similar ways to pull-ups. They can be done jumping, inclined, seated, or assisted in some way. Like pull-ups, the kipping muscle-up is the default. If none of the above scaling methods are suitable, the standard substitution is 3 or 4 pull-ups and 3 or 4 dips.
Muscle-ups can be also done on either a bar or rings. Strict bar muscle-ups are probably more difficult than strict ring muscle-ups because it’s easier to get your head and body forward through the rings. However, if you’re kipping, it will probably be a little easier on a bar because you can get more power out of your kip and the dip portion is easier. But in general it’s fine to do them on either a bar or rings.