Zoom with your fins, not the camera, whenever possible or safe. Move slow and smooth through the water while taping. Big fin kicks and other unnecessary movements will make your video rock and roll-not good in this case. Waving arms and legs will scare away your subjects. A good videographer will often be allowed to get closer to the fish because unlike many other divers, the videographer is not flailing around and scaring away the fish.
Proper buoyancy is very important, especially when taping a stationary subject.
Try not to grab on to anything living in order to maintain your position in the water. If there's surge, try taping fish that are moving in the surge with you, but watch out for stationary objects. Sometimes a fish allows you to get within 3-5 feet while taping and then starts to swim away. Don't chase the fish-follow it. A fish's instinct is to run when being pursued.