How DO I Connect my Computer to Another? IN same room?

You need a router. But, it sounds like your "modem" may be a router or a modem/router. If so, and you can access the internet on both computers through the router, the following is the wizard way to setup file and printer sharing.

Run the Network Setup wizard (found in Control Panel of XP). Tell it each of your computers connects to the internet via "residential gateway" and that you want to enable file and printer sharing. Create a disk at the end only if you have a Windows PC other than XP or 2k Pro or Vista.

Windows XP firewall (if SP2) will be properly configured by the wizard. You must uninstall or properly configure any 3rd party firewalls on each machine. Unique computer names and same workgroup, of course.

The Shared Documents folder is automatically shared. Any other folders (or drives) or printers you want to share, just right click on them and sharing ... . When sharing a printer, accept the offer to load other drivers if your other PCs have different Operating System(s).

When you first go into My Network Places there will be nothing there. The first time you click on 'View Workgroup computers' will probably result in great disappointment. It takes awhile (20 minutes or so) before all the computers in the workgroup get up-to-date and accurate lists of the other computers. Often you can speed up this process via Search for other computers.

When computers show up in My Network Places, double click on one to see its shares. If that includes a printer, you can right click on the printer to connect to it.