The GoPro HD Hero helmet camera is a great way to do that. It's cheap (relative to other underwater cameras), waterproof to 60m (200 ft) and indestructible. It also has a variety of accessories from extended batteries, to LCD preview screens that allow for flexible configurations.
When diving, how you mount your equipment can make or break a dive. If you're constantly fiddling with your gear you risk not paying attention to important things like air and depth. If it's not attached properly, you might lose it. Both will ruin your day.
My first attempt with this camera was using GoPro's chest harness. This kept the camera securely attached and for the most part out of the way. However, my BCD inflater hose would regularly flop in front of it, blocking my shot, and it was very difficult to point it at what I wanted filmed.
After having too many fish drift just outside of the frame, I decided that I needed a better solution. I picked up a tripod mount from GoPro started putting together a monopod. While there are commercially available monopod camera extenders, none of them are very well suited for diving either because they're not very durable or they're constructed of material that corrodes easily in saltwater.
PVC pipe was an excellent choice of material for this project. It doesn't corrode in saltwater and it's easy to work with. For the connection to the camera, I found a bolt with the same threading as a standard tripod at the hardware store. I secured this to a PVC cap using epoxy and a nut. From there on, it was just PVC pipe glue with segments spaced appropriately to attach retractors. I also wrapped the largest (bottommost) segment with duct tape to provide better grip.
When put together it can be used either in third person mode (left) or camcorder mode (right). The former lets me tape some cool shots of myself and my dive buddy and the latter makes it much easier to keep the fish of interest in frame when combined with the LCD panel. Combined with the amazing video quality of the GoPro then end result is amazing. You can see clips that take advantage of both of the configurations from a dive to Point Lobos in Carmel, CA below.
Technologies: GoPro HD HERO, Adobe Premier Pro, PVC pipe