Unfortunately USB networking does not work without proprietary hardware. (Your motherboard must support it...) There is firewire networking, but obviously you need firewire ports on both computers.
The simplest way (in terms of hardware) would be using a parallel cable but that would give you a maximum transfer speed of about 112 kbits per second (I think). Besides, you would need to set up the necessary drivers which I forgot how to do...
The most effective and still reasonably simple way is popping a LAN-card in both computers and connecting them with a "crossover" LAN-cable (this is very important, most cables in shops are "straight", which are to be used when connecting a computer to a HUB). LAN cards can be found for around 10 dollars apiece, the cable should be about 5 dollars. Then go and search the net for directions on how to set up a home network. It is really quite simple , should not take longer than 10 minutes or so. Firingsquad has an excellent guide (you need to dig it up in their archive though) to setting up home networks.
Basically, you need to have TCP/IP and File and Printer Sharing installed (you can check under network settings) on both machines for the LAN cards(TCP/IP will be installed automatically with the LAN-card drivers, you probably need to add File Sharing yourself), they must have different IP addresses (the last three digits only, so for example 192.168.0.1 and 192.168.0.2), the workgroup name must be the same for both machines, the machine name should be different. Then you must enable sharing for the folders you want to copy from. If this does not make sense, then read the aforementioned article on Firingsquad. Sorry, don't have much time to write...
Or... If both machines are connected to the internet, you could send the files over from one to the other using a file-sharing program or something as simple as MSN Messenger. Or you could send the files to an FTP server and download them with the other machine.
I hope I gave you something to work with... Good luck!