It depends.
Nowadays, most computers should have ethernet cards built-in. If both computers have one, then what you need is a "crossover cable," a special ethernet cable that lets you plug one computer straight into another.
If both computers have firewire, you can do the same thing with a firewire cable.
If both computers have USB, you can get a special USB cable that will allow you to do this. A regular USB cable won't work.
After that, you just go into Network Neighborhood or My Network Places and set up the connection. The best way is to tell it to use NetBIOS as there's no setup required.
Now, go to the computer that has the files you want to share, make sure "File and Print Sharing" is turned on in the Network properties, then right-click the directory containing the files and go to Sharing. Give it a share name and press OK.
You should now be able to go to the other computer, browse the network, and get the files.