The bright colors are to separate the individual sprite frames and are bright colors so they are easy to eliminate. Think of a green screen in the movies - the chances you will use one of the exact colors of the background is pretty slim, and this allows you to work within well defined borders.

Transparency is set in two ways (for single frame images, not animations). Either you create a 'transparent' background in the sprite if you are using photoshop and can do that, or else you can set the entire background to a single color and, at the upload page, hit the little 'Set Transparency' button. This takes a sample of the color in the '0,0' co-ordinate on the image, and makes that color transparent throughout your image!

For a .gif image you need to do it the first way. Apply the transparency manually and don't hit the 'set transparency' button!

Hope this helps!