Before going in to the details, I want emphasize how important research and planning is. It should be a given, but maybe you're like me and sometimes enjoy just winging a shoot, but in this case, keep in mind that when the environment is completely different, it's not quite like simply testing a new light setup.
There will be discomforts, logistics complications, and unexpected difficulties just because it's not everyday that most of us spend a few hours underwater. So make sure to read up as much as you can. It will help you prepare both mentally and logistically, and make your underwater shooting experience a smooth-sailing and fun one.
This is similar to when I do movement shots -- take a few tests and rehearse the movements with the model in the beginning. This will save time and energy as you're looking at the general picture and feel of the pose and framing. The model won't have to school her expressions or make sure her hair and clothes are perfectly in place, those things take 10 times longer to adjust in water than on land, and it gets cold and uncomfortable in water very quickly. You want to conserve her energy as much as possible.
Most of the time you'll want to sink for flexibility in angles, but it's difficult and often you'll end up floating more.
From underwater cameras, to attempting an underwater photoshoot. There are always tips but tips on how to interact with you model and the enivornment that you've been given, well sometimes thats a rare thing.