The following will explain how to create an image with a transparent background with the freely available tool Gimp.
GIF and PNG images can have transparent backgrounds. JPEG can not have a transparent background. Lets take the following example picture.
It look good on a white background but not so good on another background.
Start Gimp and open your file via File -> Open and selecting your file.
Select Tools -> Selection Tools -> By Color Select (or another method which is more appropriate to you).
Select in the Layer window Layer -> Transparency -> Add Alpha Channel. Or just use Cntr+X to cut out the selected color.
Save the file in either png or gif format.