Entering the water with your camera equipment
This usually involves a back roll from a boat. You will need to adjust your equipment once you're in the water, therefore, get someone in the boat to hand it down to you once you are ready to dive. Explain to the person in the boat how you want him or her to hold the camera, and perhaps point out the sensitive bits that you don't want knocked in any way.

 
Moving underwater and approaching marine life
Once you submerged get your buoyancy right and calm yourself down before you start shooting. In general most of marine life will let you come closer if you don't swim fast like a maniac, heavily breathing and gasping.

Once you see your subject don't swim straight to it. Give it the time to get used to you and move around it so you can approach it slowly from the front, where it can see you. A lot of marine life feel threaten of anything coming from behind and will disappear faster as you can imagine.

 
Camera angles and movements
A most often and most appealing camera angle is to shoot from a low position in a slight upwards angle. It makes you subject stand out from the environment and gives it more importance

Silhoutte against the sun can also make a very beautiful looking impression and are perfect to edit into your final movie.

Shooting with the sun in your back will lighten up your subject and bring out the colors, but make sure you don't block the light with your own body.

A combination of camera movements and angles will make your final movie look interesting. But don't overdo it with panning and tilting. Don't pan unless you have a reason, such as following a diver or showing the expanse of the reef. Pan from something to something, not from empty space to empty space.

Just pan in one direction, no multiple directions changes. When panning with swimming subjects, follow their general direction, not its every movement. If a close-up subject is moving within a small area (such as a clownfish in the anemone), let it swim within the frame and around the picture area, even if it eventually is going to leave the frame for a short time.

 
Lighting and Filters
On a sunny day with reasonable clear water, in recreational diving depths, most of video lights are of little use. The natural sunlight will provide all the necessary illumination for your camcorder.

A color correction filter ("red filter") is a must and will turn all your greenish and bluish looking pictures into something more enjoyable for people to watch. But remember, using a filter means you can't use video lights at the same time.

Video lights are useful during low light conditions such as dawn, dusk and night dives or in very deep water. In Macro- and Close up shots lights will bring out natural colors and detail.

 
Optics - Zoom
Even in really stunning visibility you will notice that there are still millions of tiny particles abundant.

One rule for underwater filming work states "as wider as better". Wide angle lenses provide you with the capability to get really close to your subject and still get it into your frame, in the same time you can avoid having too many particles in between your lens and your subject, which results in good sharpness and clarity of your picture.

Exactly for the same reason we don't want to use the zoom. Zooming through millions of particles will make your pictures appear like looked through a fogged up window. Instead use a "natural" zoom, which means swim closer if you want your subject to be closer.

 
Macro- and Close up shots
Macro- and close up shots are the one exception where zoom can be used to certain extend. For shooting most of the small stuff your wide angle lens will still do as long you can get close enough to the subject and your wide angle has zoom through capability.

For really small creatures you might want to add a flat port to your housing and exchange your wide-angle lens with a close op diopter (+2, +3, +4) attached to your housing or camcorder.

For this kind of work video lights will be a must if you want the real colors, contrast and detail in your picture.

Most of the small creatures you might want to shoot live close to the seafloor and looking through the viewfinder while trying to get a low shooting angle requires some extraordinary skill and most often end up with cramping muscles in the neck region.

A viewing aid such as an external or in build monitor will come as a great help in this kind of situation and makes shooting much easier in general.

 
Have fun and enjoy what you do without forgetting the environment.

Most important is that you enjoy what you do. Your video will come out much nicer if you have fun while filming. And there is one last very important message.