Forgive me if this is an extreme silly question :)

Let's say I have an image in gif format that has a white background color, how is it possible to make the background become transparent?

well what you need to do is hit ctrl+a to select the whole image, then hit ctrl+c to copy it. Go file --> new (the images width and height should be the default since you hti ctrl+c b4 going file --> new). Create the new document, then hit ctrl+v. Now you can use the magic wand to select the white background in behind and delete it. Now just save as a gif overtop of the one you had b4.

Hope this helps :D

Or you could do it in the "save for web" interface... it allows you to manipulate your settings for your gif, and add transparency without affecting the orgional image.

Hm... you might wanted to google it. Google make us smart :D