Anyway, video camera. What you'll need to do is buy a video camera that will fit into one of several watertight plastic housings. Granted, this ends up being a wildly expensive proposition. Ikelite, for instance, makes a wide range of housings that fit JVC, Sony, and other camcorders. Prices vary depending on the model camera you have, but you generally can figure on $500 to $800.
There is one slightly less costly option. A company called Ewa-Marine makes underwater camera "bags" of heavy, high-quality plastic, which are welded to a lens port made of optical glass. These cost $200 to $300, and will accept a wide variety of cameras because the soft sides allow you to manipulate the camera without precisely fitted levers that reach from the outside of the housing to the appropriate button on the camera. Usable water depth varies, from 30 to 150 feet (deeper it goes, the more you pay). For surfing, you could of course get by with one of the 30-foot models.