Several programs allow one system - the one with the modem - to work as a proxy Internet server for other PCs on the same network.
My favourite, based on ease of setup and price, is PPP Shar (http://www.pppindia.com). The Lite version gives the client PC (the one without the modem) Web access only; PPP Shar Pro allows the client access to mail, FTP (file transfer protocol), and even Internet-based games.
Both products are shareware; a $US25 registration fee covers three clients in the Lite version and one in the Pro. You can find both on the cover CD of PC World's July edition, due out next week.
Both versions have software that is easy to install on the server PC (the one with the modem), and they include instructions for setting up apps on the client PC so that it can access the Internet.