First get the router itself working from the desktop. Once that's working (i.e., you can get online), just goto your router settings pages again (the 192.168 things) and into the wireless setup. Make sure wireless is turned on, choose a name for the SSID (change it from 'BT' or whatever it may currently be to something you recognise (everyone can see it)), and turn on WPA encryption. Choose a password for the encryption and write it down.
Also, when you first goto the 192.168 pages you'll be prompted for a username and password, usually the username is 'admin' and the password blank, or something to that effect. Change that (in the setup pages somewhere too, once you've initially logged in), again to something random and write it down in a safe place.
Then once the internet is still working, plug the dongle into your laptop and switch on. Assuming you have Windows XP SP2, it should auto-detect it and if you go into control panel you'll find an icon called 'wireless setup' or similar. If you run that, it should search for available networks, and should find your one (have your laptop near the router at this point if possible); connect to that and enter your password when prompted, and you should be online!