Hi Peter, I am also an entertainment pro. I was a concept designer and illustrator, and I taught at Gnomon in Hollywood. Are you working in L.A.?
The drawing is good. It reads like hands so that's a good start. So what is your goal for your work? Is it for fun or are you interested in eventually doing professional work?
I learned drawing hands by drawing my own (left) hand and using a mirror to simulate drawing my right hand. I also copied the drawings of Burne Hogarth. He has a wonderful book on hands (and figures and faces) that features a cool construction that simplifies the hands. And simplification is the key.
A hand, like any thing can be broken down into simple forms. So I believe the first step to drawing something complex 'realistically' is to first see it and describe it as simple forms. For example, the palm can be described as a rectangular cube and the fingers can be simplified into tapering cylinders.
Hope that makes sense :)
Andrew Loomis also wrote a series of books on drawings. HIs approach to hands, especially the way he simplifies is excellent. Many illustrators today (especially in Los Angeles) still use Loomis' methods.
Hope that helps. Glad to see other artists here. I teach drawing myself and have some instructional material online. I can send you links if you are interested or visit my profile :)
RE: My artwork - hand drawn (pun intended)