Transparency

If your graphics have white backgrounds, they'll look okay on a white background but not any other color. Making the background transparent fixes this problem and makes your graphics look better on all colored backgrounds.

Paint Shop Pro

Open your graphic in Paint Shop Pro. Use the flood fill tool to fill the background with a color that isn't anywhere else in your image. Most people use a bright green.

Go to Image > Palette > Set Palette Transparency. If asked to convert the image to 256 colors, click OK. Choose the third option and change the color to the bright green that you used for the background.

Press Shift+V or go to Image > Palette > View Palette Transparency to show the transparent image. If the image is transparent, it will show up with gray and white boxes in the background. Save the image as a .gif.

Animation Shop

Open your picture without a transparent background in Animation Shop.

Click on your paint can tool, and make sure the to canvas color box is checked. Click on all the areas that aren't transparent. You should see gray and white boxes where the white used to be that represent transparency.

Save as a .gif. This is what my transparent image looks like:

You can see my background color behind the image, unlike before, when the white background showed up.