Test your strobe and make sure it works as it should. You would not believe how many people shoot with a strobe without even knowing that it’s not firing strong enough, or not syncing, or even not firing at all!
Do not use Auto ISO. If you are shooting manual, which is the probably the best mode to use underwater, quite often divers leave the ISO on Auto. This setting causes the camera to automatically set your ISO way to high, letting in too much ambient light and messing up your photos. Unless shooting video, do not set your ISO on Auto!
Buoyancy is the single most important skill to master as an underwater photographer. I cannot stress this enough – nothing will improve your underwater photos as much as getting to that point of perfect control over your buoyancy underwater.
If you are not there yet, practice! On every dive, every time.
You want to reach a point where you can shoot a macro photo, a few inches away from a subject, without touching anything (yes, not even a finger) and then backing away elegantly using the back-fin technique.
