You need what's called a "router" which sits between your PC and modem, then you plug the other PC directly into the router. To keep things tidy and simpler, a better deal is to get a router with ADSL modem built-in, which you connect to your phone-line then connect both computers to the new router. The existing router then becomes obsolete.
An even better upgrade (and the best), is to get a wireless router/adsl modem combined, plus a wireless adaptor for the second PC. Your main PC plugs into the router/modem with ethernet cable, second PC connects via it's wireless adaptor. This setup is especially handy if the second PC is in a separate room where a wired connection is impractical.