The following describes the movement as it is broken up into small pieces, however, this is a plyometric type of movement in which one needs to explosively move through each phase in order to complete the exercise. The muscle up consists of 4 steps - A hang, an explosive (kipping) pull-up, a triceps contraction and a lateral grip dip.
1) Hang on to the widest grip pull up bars.
2) Making
sure your whole body is tight, swing your legs forward. While they are
swinging back, prepare yourself to explode upwards.
3) As your legs go past neutral hanging
position and start to give your body upward momentum, pull upwards in an
explosive burst. 
4) Use this momentum to
carry your body above the bar where you bring your wrists around the top of the
bar and push up into a dip. Repeat.
Sanjay's Expert Trainer Tip: Make sure you pull up behind the bar and not
underneath it.
