How do you save a cutout?

I see lots of cutouts (graphics with no background) in various galleries but I can't figure out how to make one. I can cut an image out and paste it as a cutout but when I save it, it looks and acts like any other picture with a white background.

Howard

From the FAQ.

Transparent gifs in Photoshop < http://www.photoshopcafe.com/tutorials/transparent/transpare nt.htm>

Photoshop's native format, PSD also supports transparency.