On the computer that has the modem, go into the properties for the connection and somewhere on the Advanced tab you'll see an option to share the Internet connection.
Hook up the other machine to the machine hosting the connection and if all goes well, that machine should now be able to access the Internet (a couple reboots of both machines might be required to get Windows to co-operate). If it doesn't work, post back. BTW, when you say modem, do you mean 56 K or DSL/cable?
A downside to this approach is that obviously the computer with the modem needs to be powered on to access the net from the other. If this will be a problem, you could also invest in a NAT router with a DSL/cable modem built into it, then it's just a case of plugging each machine into the router with an Ethernet cable. There are several other advantages to a hardware NAT router too, but obviously they aren't free like XP's software NAT is.
