To get that kind of a look I'd start with a spotlight like a PAR 46 or 56, to cast the disc of light down onto the set but leave the edges dark.
Then a couple of strategically placed rim lights or edge lights (it means the same thing). These would be lights placed on the side of the set away from the camera, pointing toward the camera at an angle, so that they cast a rim or edge of light on the objects (including the puppet). In addition to that, you might also want some kind of soft lighting - very diffused and very dim - coming from the front to fill in the solid blacks if that's the effect you want. It would be good to be able to control the brightness of this fill light - so either a dimmer switch or neutral density filters would take care of that.
You might also want to use blue filters over your lights - this can help though moonlight actully looks white. Its kind of an accepted canon - sunlight is yellow, sky light is blue, and night shots are often tinted blue. But the plain white light in that clip looks great.
Like the Stridemeister said.
I usually go with the conventional blue cast to the moonlight, though in varying degrees - sometimes subtle, sometimes just plain theatrical like in this pair of images. (How do you embed images in this message board so they show up? Never mind, you can click on it.)
Thanks a lot, I've been working with a blue light and it just coats everything with a bluish purple hue. Can't wait to give these tips a try. Also thanks Nick for the image, I was wondering about displaying a moon as well and was thinking about doing it digitally but I'm trying to stay away from special fx so that was a big help also. Can't wait to take some stills and share them with you all,