Brian Skerry is a photojournalist specialising in underwater and marine-related subjects and stories. He works for The National Geographic magazine and he continues to pursue stories that will increase awareness about the sea.
Here's his advice:
It's sometimes easy to get so caught up in the moment of photographing interesting subjects underwater that important elements of composition are overlooked. A couple of key things to be mindful of are negative space and separation.
Negative space is defined as everything in a photograph that is not the subject. Although the subject is important, it is often the negative space that can make a photograph exceptional. When shooting macro photos for example, novice photographers often spend most of their time searching for subjects only. Experienced photographers on the other hand, will often spend more time searching for negative space then search for subjects within or wait for a subject to swim into the frame. Regardless of what type of photograph you are making, the care you take in photographing the negative space is often as important as the care you take in photographing the subject itself.
Separation or contrast is the term applied to the degree that a photo subject can be distinguished from the background and is a key element in photo composition. When shooting many underwater subjects, especially animals, it is easy to become excited and forget about the background, but paying attention to separation will definitely improve your results. When photographing divers or animals in the water column it is often helpful to shoot at upward angles in order to "separate" the subject from the darker background water. By shooting at slightly upward angles, the darker subject contrasts well against the lighter water towards the surface. Even when shooting macro better images will result when the composition is framed to eliminate distracting backgrounds. This might require viewing your subject from many perspectives in order to arrive at the perfect angle.
So even if the subject is fantastic, pay attention to composition to make sure you create a perfect picture of a perfect subject!