The easiest way is to use a tracking telescope with a modified web camera to shoot video. If the image scale on the chip isn't large enough, you can add a Barlow lens or two between the telescope and camera.
You'll need to experiment with exposure time per frame, as it'll depend on the f ratio of your optical system, and the gain of the camera. You'll probably end up shooting between 1/15th and 1/5th of a second per frame.
If you need to use a garden variety video camera that doesn't allow you to replace the lens with a telescope, you would look for help with "afocal" imaging through a telescope. You'll need an adapter that screws onto the filter ring of the camera and , aims it at an eyepiece, and fits into the eyepiece holder of the telescope. About ten years ago, I did this with a JVC camera that had a "night vision" mode, but the weight of that camera tended to make balancing the scope so it tracked properly more of a challenge.
Here's a shot a friend and I took of Jupiter and Io using a 140mm f7.5 apo refractor an Astro Physics Barcon barlow and a TMB 1.8x barlow (two barlows at once) with an Imaging Source dbk 21AU04 camera. While this is a stacked shot, it was made from the best frames in a minute or so of video.
< http://www.holden-insurance.com/jupiter8109I.bmp >
The Imaging Source camera can be thought of as a "Scientific webcam" that accepts C mount lenses. It's very well made, and comes with software designed for astronomical imaging. The Celestron NexImage someone else talked about would be a "budget alternative". (I have one of them too)
If you don't own the equipment, it would be worth tracking down a local astronomical society. They may have members who already own most if not all of the equipment you need, and if you're friendly, they'll probably be willing to help.
Here's a link to an on line resource that'll help you track down your local astronomy club:
< http://www.skyandtelescope.com/community/organizations >
Good luck.