I agree with ethel.
you'll have a modem connected to your comptuer right now, yes? hopefully with an ethernet cable, which looks like a thick phone cable (same type of connections). all you have to do is connect the modem to the wireless router, and then get a cable to go from your router to your computer.
then as ethel says you can get a wireless adapter to fit in the other computer:
http://www.scan.co.uk/Products/ProductInfo.asp ?WebProductID=219716
you have a few things to check first though: make sure your modem connects via ethernet and not USB. if it connects via USB you're probably better off buying a wireless router+modem in one (making sure you buy either ADSL or cable as neccessary). if you need to buy another ethernet cable, go for something like this one:
http://www.scan.co.uk/Products/ProductInfo.asp ?WebProductID=60009