Creating artificial light underwater can bring a whole host of problems, mostly because many underwater photographers use the on camera flash, not only is this quite harsh on the eye and resulting image, it can over power the colour range and only make a small section of your image colourful. Certainly if you’re using a wide lens.
Adding two off camera flash heads that sit either side of the camera, one slightly higher and one slightly lower will create a lovely wall of light that will last for around 3 to 5 feet. There are many guides out there on the web that will contest flash should be used this way and that way, however I have found “spotting” your flash in one area alone can be very limiting and increasing your chance of highlighting small items in the water you may not want in your image.
Defusing the light is imperative to your success as well, making a wide spread of light is one thing but using the housing defuser will also create a softer feel to your composition. One hack that I use for underwater flash is applying clear sticky tape to my flash head which is normally enough to defuse and not block a whole stop of light from entering the frame.
Also with flash stay limited by the xsync of the camera, typically this is anywhere between 1/200th and 1/250th but should be enough to freeze any subject and if you wanted to keep the flash in TTL mode (nothing wrong with that) then do so and make sure the flash is set to underexpose by 1/3rd of a stop.
Doing so means you will never over power the scene and if it’s a tad dark you can always recover the scene in post production. TTL does have a habit of over exposing underwater, if you’re using manual flash then set to ½ power depending on your unit but that most powerful heads I set to ½ power and then adjust my camera settings or close up the aperture when needed. That way I just have one dial to worry about and not two.
Colors will also be more sensitive to shutter speed than aperture especially the colour of the ambient water around you, slower shutter makes the scene more blue, faster more green.
Another way is to use continuous lighting through LED panels or light bars that are waterproof, some need housing, some don’t the draw back here is pretty much everything in the water will see (and hear) you coming.