How big are the files?

The cheapest way likely would be to buy a cross over cat5 network cable, you can then plug it directly into the ethernet ports on each computer and share out a folder on the destination computer and copy the files to the shared folder. Make sure when you share the folder you give full access to all users to change files (on xp there's a little check box when you share a folder that says something like 'allow users to change files'. Also make sure each computer has the same workgroup name and a unique computer name and are part of the same ip subnet.
For example setup one computer with the following:
ip: 192.168.1.100
subnet mask: 255.255.255.0
gateway: blank

Then setup the other like:
ip: 192.168.1.200
subnet mask: 255.255.255.0
gateway: blank

Then the two should see each other through windows explorer.

Here's a link that should help you if you need to go this route:
http://www.cellarstoneindia.com/cable_pdf/Direct_Crossover-_Windows_XP_To_Windows_XP.pdf

If the files are less then 1GB in size then the easiest but more expensive way would be to buy a 1GB usb memory stick (I think you can get them now for about $79)...you could also buy 512MB or 256 MB or whatever you need...then when you plug them into the usb port they will show up in explorer as a removable drive and you can copy the files from the source computer to the usb key, then unplug, plug into the destination and copy, repeat as necessary....this solution is probably the easiest of the two but if the files are smaller then 1GB in size.