Alice,
The key to getting dark backgrounds in photos is to make sure that there isn't enough light to light it up. You can do this several ways.
1. Use a dark background. I have a 3 ft. x 3 ft. piece of black velveteen that I bought at wal-mart for a few dollars. I can hang it over a chair back or something similar (I have tacked it to the wall before) and then photograph the animal on a stick or similar object a few feet in front of that background. That will give you a nicely lit animal with a pitch black background. They key is to make sure the black background is far enough away from the subject.
2. You can also make any background darker by reducing the power of the flash or by reducing the amount of light reaching it. You can do that by distance - the further away the background is, the darker it will appear. You can also do that by closing down the aperture (use higher f/stop numbers). Generally, if you are using flash, the higher the f/stop value, the darker the background.
3. You can also darken the background by moving the flash in from a very sharp angle. That is what I did in the Blackbellied Salamander photo. The flash is held in my hand way over to the right and above the camera so that light doesn't fall onto the background. Combining that with a high f/stop gave me this effect. Of course, you need a flash that you can take off the camera for this.
Part of the key of taking good closeup shots with a point and shoot digital is knowing the macro limits of the lens and then knowing how to control the depth of field using your shutter speed and f/stop. The hardest part of getting good macro pictures with a point and shoot is getting the light correct. Many times you have to reduce the power of the flash (flash exposure compensation). This will prevent you from blowing out the light areas of the picture.
To be honest, the real key is practice. Remember, it is digital so film is free. Take a small object and photograph it over and over again with different conditions and from different angles. Don't try to use a living organism, just use an apple or something that doesn't move. Take notes as you shoot and you will figure out what you can achieve with your camera.

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Chris Harrison
San Antonio, Texas