Tip #1 - When shooting pictures underwater, follow two important rules. Get close to your subject and shoot at upward angles. This will allow you to fill the frame and get separation of your subject from the background.
Tip #2 - Use a Color correcting filterA secret tip to get better looking photographs is to use underwater color correction filters on your camera, which are essentially red filters which can be screwed onto the front of your camera’s lens that corrects the color balance by reducing the cyans or Blues in your pictures. Choose a filter density according to the depth at which you will be photographing and the color of the water, ranging from dark blue to green.
Tip #3 - While out on the dive boat be sure to keep camera gear out of the sun and away from heavy dive gear like scuba tanks and weight belts.
Tip #4 - When travelingwith underwater photography gear, be sure to pack carefully to protect your gear. Be aware of current air travel restrictions and pack accordingly.
Tip #5 - Remember what you learned in your scuba diving class. You are a diver first and then a photographer. Your safety and that of divers around you depends on keeping this in mind at all times.
Tip #6 - Make sure your camera flash is turned on, preferable in "forced flash mode."
Tip #7 - Try to fill your frame with the subject. Don't shoot "down" at the subject.
Tip #8 - Make sure the subject's eyes are in focus.
Tip #9 - Get your diving skills down before you start using a camera underwater.
Tip #10 - Practice topside with your camera inside the housing. Try taking close-ups of flowers and household objects.
Tip #11 - To minimize backscatter, buy an external strobe/flash and position it away from your underwater camera housing.
Tip #12 - Set your camera to the highest resolution.
Tip #13 - Use auto white-balance when using a flash/strobe, and custom white balance or underwater mode when not using a flash.