1. Avoid using a flash or use a flash that can be moved above the image you are trying to photograph (keep in mind a flash can stress animals, cause a glare off the aquarium, and may not be permitted). Using a lens hood can also help reduce glare from the glass of an aquarium. If there is too much natural or outside light this can also cause a lot of unwanted aquarium glare, a dark room with the aquarium light alone can often be more ideal.
2. A fast lens with a big aperture, preferably an f/2.8 or faster (the lower the f number the faster the lens, and a big aperture will allow for more light if you can't use an adjustable flash).
3. A fast Shutter speed (to avoid blurry images of moving fish) and an of ISO of 800 up to 1600 because a fast shutter speed will cut down on more of the light you need so it's important to crank up your ISO to balance this out.
4. If you can later edit your processed images using noise reduction this will also help to create a clearer final image (using a circular polarizer lens cover may also help cut down on noise) . Also editing your images later on can create more vibrant images (as often times a lot of color can get lost through aquarium glass).
5. Keep your camera stable (tripods may be restricted inside the aquarium). Pressing the camera lens against the aquarium can help stable the camera against the glass (use a UV filter to avoid debris or scratching the lens). Try to keep the camera perpendicular to the glass in order to avoid distorted images of your subject.
6. Avoid using an Automatic Focus (AF). Use a Manual Focus (MF) with a short depth of field as your object is constantly moving and using the AF will focus too soon before you'll be able to get a clear shot at the moving subject (doing this will help reduce blurry images). Be sure you get the correct White Balance set on your camera, you may even find using a Fluorescent setting on your camera can help in photographing your subject matter (it may help reduce blue tint). Also try using the Fast Action mode on your camera if available. Also if your camera has a Macro function this can also help photographing your subject at close range).
7. Have Patience. Take many photos. Photograph at different distances. Don't just photograph fish but also their habitats which can be very beautiful as well. Carry spare batteries and memory cards.
8. Using a DSLR camera should be more beneficial in low lighted conditions than other cameras.
9. Try to wipe off the area of glass you're photographing at, if it's dirty your camera will probably end up photographing that into your image. When the aquarium water is as clear as possible it will also allow for better looking photos.