Photographing underwater is a craft unto itself, and there is a lot to consider compared to shooting on land. Water absorbs lights of longer wavelength, i.e. warmer colours, so your photos taken from a distance underwater would inevitably look blue.
This is why the first and most important technique to remember is to get close and use a flash. It is recommended to be at most 1 metre away from the subject, ideally even closer, to reduce the distance that light has to travel through water. Turning on flash is almost mandatory to give the subject much-needed colour richness, unless you are in shallow waters where daylight permeates.
Another related tip is to bring an external strobe light. The convenient internal flash can sit too close to the lens, causing reflection from water particles, often tarnishing the picture with white specks, an effect known as backscattering. This can be minimised by positioning the strobe light away from the camera.
In general, you will want to have your ISO as low as possible (since you would be using a light source) and shoot on eye level, of or from below the subject, to make a nice spatial composition. Remember, these are just some rules of thumb for when you are starting out, so don’t be afraid to experiment, get creative and go with the flow!