I can give you some tips I've learned from years of photography and graphic design that I think apply to video as well (I have done some videography as well and am looking to get back into it in a major way shortly).
* Visually, less is more.
* Raw footage-wise, shoot as much as you can.
* Go for the interesting angle rather than the boring "snapshot" type angle. When you could shoot something straight-on, shoot from below or the side instead. If you're shooting through a doorway inside a wreck, maybe you strategically include part of the doorway in the frame.
* Something which I think is called the "rule of thirds" which very basically says that you should try not to center everything, but rather frame things so that they are more towards one of the four sides or corners of the frame, ie off-center
* Pay attention to lighting. Sometimes having something half or mostly in shadow makes your subject look much more interesting.
* Try to find an object that dominates your frame
* Find a second object and try to set up some kind of visual relationship between the two, balance them off one another.
* Look for the imaginary "lines" and "shapes" that your subject makes. Example: Shooting down the length of a wreck so that the sides of the boat form a slanting "arrow" shape against the blue as it recedes from the camera is a lot more interesting than backing up and just shooting it sitting there horizontally across the screen. The same with those "alleys" of sandy bottom between two large outcrops of coral.
* Don't move the camera all over the place aimlessly, give the viewer's eye something to latch onto, and time to assimilate what they're looking at.
* If you must pan, pan slooowly
* Sometimes a stationary shot is a good thing.
* If your housing gives you a zoom control, for God's sake don't use it while shooting!
* When you get into editing (and this is just a personal bias coming from watching too many home movies) don't get distracted by fancy--read "silly"--transition effects. Contrary to what the advertising tells you, they don't make your home movies look professional; they make them look like home movies with silly transitions.
* One more personal bias: put divers in with your undersea wildlife. And I don't mean unwitting divers in the distance who don't know they're being filmed and who you only see for two seconds while your camera roams around. Film your dive buddy, or some other willing soul on the boat, interacting with the fishies; swim around him/her, get up close. Encourage the audience to think "that could be ME!"
I don't necessarily advocate trying to ape other people's work, but try watching some movies and documentaries about the ocean and study how the great professional underwater cinematographers like Al Giddings and Jordan Klein shoot. Try movies like
The Deep, or any of those National Geographic videos. You don't have Super-Panavision, for sure, but you can at least see how they choose to frame their images and so on.
cheers
Billy S.