I think this exercise, strictly speaking, should be done using gymnastic rings. I will find a video of this being done, but for now am focusing on the version that uses a bar, since that is what I do.
Using a Bar
This is the basic form using a bar - he does swing a little bit, but not enough to classify this as a 'kipping' muscle up (see lower down.)
Jump-Assisted Using a Bar
I don't have a video of this, but essentially this involves standing on a box under a bar and jumping into the movement so I can provide additional momentum to allow me to perform the muscle up. By reducing the size of the box, then the extent to which I rely on a jump, I hope to progress towards the unassisted version.
Swing-Assisted, Uneven Muscle Ups Using a Bar
This was how I achieved my first muscle up - by swinging and then doing an uneven muscle up so that my strongest arm took priority. In other words, I just did my damnedest to get up there. Now I can work backwards from here and try to tighten up the form.
These are a lot like dips - you start in the normal end position - arms straight. Find a wall or other platform and then get yourself into the position as if you had just done a successful muscle up on it. Then lower yourself as far down as you can go whilst still comfortably then pushing back to the straight-armed position. To progress, increase the depth to which you go before pushing up.