You may also want to check out this article on T-Nation about muscle ups:
The muscle up involves just about every muscle in the upper body. Your entire back, your abs, every muscle in your arms, etc. The video embedded in that article has a good approach to the progression needed.
One of the keys to being able to switch smoothly from pullup to dip is the false grip mentioned in the T-Nation article. However, the following is a progression that can work:
- Train pull-ups and dips separately on a straight bar--using the false grip for both. Be strict (no kipping). Get to 15 at once on both.
- Train your pull-ups to get your chest touching the bar, and your dips down to touching your chest to the bar. Get to 15 at once on both.
- Use kipping to help with the transition from pull up to dip. Mental cue: "roll the bar". The bar won't move, but if you roll the bar toward your chest, it will help get your body into the dip position.
- Phase out the kipping and do them strict.