Macro photography, taking close-ups, is the simplest way to get good results every time underwater, especially when conditions are poor.

A classic macro shot - the fish was less than 2cm long
The two things which add the most difficulty to underwater photography are limited visibility and the amount of floating detritus in the water, and both of these problems are reduced or eliminated entirely simply because you need to get so close to your subject.
All compact cameras have a macro mode. Usually this allows the camera to take sharp pictures of subjects at around 20cm from the lens with the lens set at the wide-angle end of the zoom, or somewhere between 30cm and 50cm with the lens set to the telephoto end of the zoom, though on some compacts the lens has to be set to wide angle in order to use the macro mode.
You can see the effect of using the macro mode with the lens set to either wide angle or telephoto in these two pictures:

Olympus C5000, zoom set to wide angle and the macro mode turned on - this picture of a 2p piece was taken from as close-to as the camera would allow

Olympus C5000, zoom set to telephoto and the macro mode turned on - the same 2p pieces as above, and also taken from as close to the subject as the camera would focus.
There isn't much to choose between these pictures in terms of the size of the 2p coin, but the perspective is different. See how much flatter the image taken at the telephoto setting seems? That may or may not be a good thing, but it's as well to be aware it happens.
Minimum focusing distance in macro varies from camera to camera. Some compacts will focus as close as 1cm from the lens. My Olympus won't go that close in standard macro mode, but it has a has a Super Macro mode which sets the zoom to wide-angle and lets me focus on objects just 4cm from the lens.

Olympus C5000, zoom at wide-angle and Super-Macro mode turned on, same 2p piece
When the supermacro setting is used the subject looks much larger. The downside is that the camera has to be very close to the subject, which means that the built-in flash will probably miss the subject unless a diffuser is used. Diffusers are usually supplied with housings, they're the piece of white plastic designed to sit in front of the flash. Diffusers are better than nothing, but often still don't allow very close subjects to be fully lit, so you'll need an external strobe, unless it's bright enough to use natural light. Trouble is, when the camera is so close to the subject it can be difficult to position an external strobe.

Very short camera to subject distance with Super-Macro, with some cameras this distance can be even smaller
The solution is a Macro Lens. Add-on external macro lenses work by reducing the maximum distance on which the camera lens can be focused and will work at all zoom settings, though they'll usually deliver best results at the longer end of the zoom.
The camera does not need to be set to macro or super-macro mode when you use a macro lens!

Olympus C5000, lens at telephoto setting, plus an Epoque macro lens

The camera is further from the subject even though the image is larger, making it easier to position an external strobe. The internal strobe cannot be used because the macro lens is in the way and prevents light hitting the subject, but it can still be used to trigger an external strobe.
Depth of field is very small when you're shooting macro - this is the distance in front of and behind the plane of sharp focus which appears acceptably sharp. You can see it very clearly in this shot, taken at f4.8, the maximum on my Olympus at the long end of the zoom; the central feather of the three making up the design on the coin is sharp, but both front and rear feathers are out of focus.

This is characteristic of macro shots, and if you review the sequence of shots above you'll see that the larger the image the shallower the depth of field. The only way to increase depth of field is to close the aperture, say to f8, the smallest available on most compacts.

These shots were all taken with the coin at 45 degrees to the camera, and even with the minimum possible aperture there still isn't much depth of field. The way around this is to shoot subject which are as parallel to the camera as possible, like this. Edge to edge detail, and if you look at the real life examples you'll see they're all pretty much flat to the camera except the crab, and on him the area in focus is the plane including the eyes and the front of the shell and legs, with focus falling away behind.

SLR Macro
When you use an SLR the depth of field can be wafer thin. Here's a shot of the 2p coin set at an angle and made with a 105mm macro lens at f4 and at 1:1 magnification, which means the image is the same size as the subject.

Strobe position
The simplest place for a single strobe is directly above and slightly behind the camera lens, with the flash pointing ahead and not down at the subject to avoid creating backscatter, like this:

(Note that the pictures show my SLR rig - lighting is the same, however, so the camera being used isn't important)
This picture was taken using one strobe centrally placed:

Less than 2cm long, these flabellina are common in the Red Sea, as long as you know where to look!
With twin strobes a simple 'one either side' arrangement can produce good lighting

This picture was taken using the 'one either side' arrangement, but with the power to the left strobe turned down to produce better modelling in the subject. If you do use a two strobes keeping the power outputs different is a good idea to allow shadows and the shapes of your subjects to be easily seen

Just to show that macro opportunities exist everywhere, this little horror was in a local lake!
Here's an arrangement that can work to get even more modelling and 3D into your shots

Either light can be the main source of illumination simply by altering the relative power levels of the two strobes, the second unit fills in the shadows thrown by the other to prevent large areas of black dominating your picture

Taken with a similar set-up to the last one shown, with the main light on the right to emphasis the texture of this decorator crab, plus a central fill-in to avoid harsh shadows