There are two types of background effects you can produce, either a lighted background or a jet black background. A black background is easier to achieve. All you need to do is make sure the rear aquarium glass panel has nothing immediately behind it. When you compose your shot, ensure that you have a clear view of the back panel in the background. The flash will produce enough light to correctly expose your main subject but the background will appear black; this is because there will be nothing present in the background to reflect back the light from the flash. Many photos taken in open water will appear to have dark backgrounds for a similar reason.
The other alternative is to place an artificial background behind the rear panel. It could be made of paper or cloth but should have a color and pattern that will appear natural. Ideally, you want the background to be out of focus. An out of focus background will be harder to identify as artificial and will also have a smoother more even appearance which will be less distracting. Remember, as always, you don't want anything to draw attention away from the main subject of your photo. Getting your background to be out of focus can be a little tricky since the distance between your subject and the rear panel will not be huge. You may need to set your aperture to smaller value like F5.6. The higher the level of magnification you are using, the easier it will be to have the background out of focus. Use depth of field preview if you have this feature to see if there are any light or dark patches in the background area that could be distracting.