so here's what you do:
1. Connect the ADSL router (make sure you get the wireless version)to your ADSL enabled phone line. You'll need to connect the router to a computer whilst you configure it - that's simply so that you can see the HTML page that contains the graphical interface where you enter details of your ISP username and login.
2. Once that's done the router will automatically connect when it's booted, and will maintain the connection for as long as you leave it on.
3. I suggest that you buy a USB wireless networking adapter for the PC and a PCMCIA wireless network card for the laptop. The laptop will work equally as well with a USB adapter, but you'll need a spare USB port for it.
4. Install the software on both the PC and laptop BEFORE you plug in the USB adapter/PCMCIA card adapter.
5. Plug in the adapters when prompted, and you'll find you can use the broadband connection on both of them.
It doesn't matter if the main machine is turned off - the connection will still work on the laptop. That's why you need a separate adapter for the PC. You can always connect the PC to the router by cable, using a LAN card if you wish, but the USB adapter is cheap, works perfectly, and there's no cabling to worry about.