If you would like to setup your network to automatically dial up the Internet, either the Diald demand dial-up or new versions of the PPPd packages will be of great utility. Both Diald and PPPd are very powerful in their configuration flexibility.
To setup PPPd for Dial-on-Demand, pease check out the PPPd Homepage
Once Dial on Demand and IP Masq have been setup properly, any MASQed client machines that initiate a web, telnet or ftp session will make the Linux box dynamically bring up its Internet link.
There is a timeout that will occur with the first connection. This is inevitable if you are using analog modems. The time taken to establish the modem link and the PPP connections may cause your client program (WWW browser, etc.) to stop. This isn't common though. If this does happen, just retry that Internet traffic request (say a WWW page) again and it should come up fine. You can also try setting echo "1" > /proc/sys/net/ipv4/ip_dynaddr kernel option to help with this initial setup.