I have bought a bunch of doverpublications.com CD-ROMs of
permission-free graphics.  But when I import them into my PrintShop 21
Deluxe documents, the backgrounds around the images are white.  I want
to know how to make these backgrounds transparent so that the
background will match the background of my PrintShop project.

If you have access to Photoshop or a similar program you can convert
the graphic to a gif and select the white area to be transparent.

Oh, and you can also make the background transparent in Illustrator or InDesign.