Rules-of-thumb for use:
Use GIF when:
Graphic of inanimate object(s) with minimum number of colors and no transitions. If for web: reduce the numbers of the colors in the palate to the minimum will reduce the size (think loading time) of the graphic.
Desiring a transparent background so as to not compete with the background of the screen or picture you are creating? In edit mode, choose transparency.
Will be using this graphic as part of an animation? GIF (and now JPG2 and PNG will do this, also).
Use JPG/JPEG when:
Graphics/Images of persons, landscapes, etc. where transitions of colors need to be smooth and not "blotchy"
Graphics/Images have many, many colors demanding smooth transitions of colors.
Use PNG when:
Most of your users have installed one of the two latest versions of their favorite browsers.
You need to have a higher resolution graphic.
Your image needs a high resolution and transparency.
Most image software programs can save your image or graphic in any or all of the above formats. Most will use the "Save As" and offer you a list of formats in which to save your image or graphic.