The most important hints for unterwater photography from my point of view:

1. Never touch anything during photography - If you cannot take a picture without lying within the corals don't take it. And don't put any animal in a better position for taking pictures.
2. The substrobe should point as directly as possible to the motive. This is very important for wide abgle pictures because there the strobe should be exactly centered.
3. Try to expose the motive you want to photograph. Look at the Christmas tree worm. There you see that because of the dark background the eye will not be drawn away from the motive. If it is not possible to expose the motive then check the background. If it is very light (i.e sand) the picture will be probably not worth to take.
4. Never take a picture from above or from the rear of a fish.
5. If you approach a fish try not to breath :-) and try to dive slowly without hasty movements. Remember that in the ocean normally the bigger eats the smaller and you are most of the time bigger than your motive. If you are able to approach then take several pictures starting from a greater distance and the going slowly closer until the fish hides. Go as close to the motive as possible and remember that the picture you see through the lense (SLR camera) is most of the time smaller than the image on the film.
6. to be continued ...