You need to enable "Internet Connection Sharing" in the PC that has the actual internet connection. How you do this depends on the version of Windows that it is running.
To enable “Internet Connection Sharing” in Windows XP, open the Network Connections folder, right click the actual internet connection (modem connection), select Properties and then the Advanced tab. Tick the box “Allow other network users to connect through this computer’s Internet connection”.
When you enable “Internet Connection Sharing” on the Internet connection in the “host” PC, it automatically configures the Local Area Connection with the IP address 192.168.0.1 and subnet mask 255.255.255.0. The “client” PC’s Local Area Connection should be set to get its IP address automatically, which it does by DHCP from the “host”. Also, if you run the Zone Alarm firewall in your “host” PC, the Internet Zone Security level must be reduced from High to Medium or “ICS” traffic will be blocked.