Major thing to note:
Do you have ADSL broadband (down your phone line, from BT or Tiscali or someone), or cable broadband (from NTL or Telewest etc.)?
If you have ADSL broadband, then get a router with ADSL modem built-in, like this one:
http://www.ebuyer.com/UK/product/52244/rb/2520 6904245
If you have cable, then just get a router on its own, like this one:
http://www.ebuyer.com/UK/product/48546
This connects straight from your phone line, or straight from your cable modem respectively. Then you connect your computer(s) from the router, either with a wired connection or wireless. If you can connect with a wired connection, then do this (i.e., try and put the router near your main computer).
Then you need to make sure that your computers that you want to be wireless have wireless capability. Most new laptops now do have this, but older ones and desktop computers may not. If not, you'll need something like this:
http://www.ebuyer.com/UK/product/60014
Or if you're feeling a little more adventerous and want to make a desktop PC wireless, something like this:
http://www.ebuyer.com/UK/product/50127