If you see something interesting try to take several pictures of it from different angles. In general, for every good picture, you will have two or three pictures that you will throw away. Don't let your only shot of that great moray be one of the throw away shots. The second part of becoming a good photographer comes after the prints have returned from developing. Spend some time with each of them and study them for their good points as well as their flaws.
Every picture contains a lesson in it about how to become a better photographer.
There are plenty of good books out about photography and a few about underwater photography. For the Aquashot photographer, I would recomend books that focus more on composition and less on the technical aspects of the camera itself. Two books worth considering are Howard Hall's Guide To Successful Underwater Photography and Norbert Wu's How To Photograph Underwater. While both of these books discuss the technology of photography, they also have a wealth of examples of great shots along with descriptions of what makes them good. Study and learn from those examples.