I had always wanted to do muscle-ups, but was stuck for a very long time. These are the lessons that I learned along the way:
1. Pull-ups and muscle-ups are very different. I thought that if I did a lot of strict pulls-ups, I would naturally progress to doing muscle-ups. Not true at all. I could do multiple weighted pull-ups (as in +30kg) without being able to do a single muscle-up.
2. Muscle-ups are 95% technique and muscle memory. Jumping muscle-ups from a low bar help develop this muscle memory.
3. Not exactly sure why, but bouldering/rock-climbing REALLY helps unlock muscle-ups. Climbing had the effect that I expected pull-ups to have.
4. Before moving on to the rings, make bar muscle-ups as clean as possible. Focus on not swinging at all at the bottom.
5. Resistance bands are the only way that I was able to work technique/muscle memory. I would have never unlocked the ring muscle-up without resistance bands.
6. Weighted pull-ups make you stronger. Weighted muscle-ups simply force you to use the correct technique.