Swapping files from one computer to the other... but how?

[The Alcotroll]

It should be a simple problem to sort out, surely, but I can't for the life of me get it to work.

I have two computers sitting side by side; one old, one new. The old one has some pretty important files (A couple of PDFs and a few word documents), and I want to transfer them onto the new. I've a USB cable (at least, I think that's what it says. It fits into the hole decorated with a picture of three computers joined together...) connecting the two, but I can't see anything in 'network places'. I've followed the (supposedly) idiot-proofed instructions for setting up a 'home or office connection', but drawn a blank.

Any help would be gratefully recieved.

Edit: And before anyone suggests using floppy disk or CD as a stop-gap measure: The new one doesn't have a floppy port, and I broke the CD-writer on the old.

[Titus]

Do you have a thumb drive or memory card to put the stuff on?

[The Alcotroll]

Doubt it. Not sure what they are, mind, but If I had one I'd probably know about it.