if you only have one computer, then yes, you would run a cat5e patch cable from the cable or dsl modem, to a NIC (network interface card) installed in your computer. You probably already have one, the connector looks like a really big phone line connector. You may need to configure the connection, but usually windows xp will recognize what's going on and install the necessary drivers for you.
If you have more than one computer that connects to the net through the one modem, then you need a router, or in a simpler case, two nic's installed on the first computer that connects to the modem (this computer then uses microsoft's shared connection driver to act as a router, and another computer can connect to the main one via the second installed NIC via a cat5e crossover cable). While it's possible to have several NIC's for several connections using the main computer as a router, the usual solution is to use the second NIC to connect a simple hub, then several computers can connect to the hub, into the main computer, and all share internet access. The only drawback of course is the main computer has to be on and connected before the others can connect (this is the advantage of using a real hub, all computers are wired to the modem, so, any one computer can be on and still connect).