Belkin F5D7132 Wireless Extender
These things pick up a wi-fi signal, boost it and then re-transmit it.
I bought this off e-Bay as, after downloading the manuals for various ones, it seemed like the simplest to set up.
When I got it couldn't do a thing with it and I wondered if, being second-hand, it was faulty.
More Googling revealed many accounts of people having trouble, or being utterly unable to set them up.
I eventually found a review on American Amazon where somebody had written a guide on how to do it. Following these instructions I got it going inside ten minutes and it works fantastically well, better than I'd ever expected it to.
Given the capricious nature of the internet I've downloaded these instructions and add them here as a PDF file. I take no credit for their composition and certainly don't hold the copyright. As the author went to the trouble of writing them for the aid of his fellow man I can't see any objection to my making them available here.