Yes. Connect your laptop to your modem and install the broadband software to it. When a connection is made (or just before) you will be asked if it is a new installation or a second computer using an existing account. Obviously click the latter. Your laptop can then access tinternet using same login / password etc as your desktop.
You could get a wireless broadband router which you attach to your broadband then put wireless cards in your PC and laptop then both will have internet access (without unsightly wires). I think BT do a kit with all you require which can be bought from PCworld.
It depends whether you're on Broadband or Dialup really. For dialup you can use Analogs free proxy, or if you have Broadband, I'd suggest a router.
Both are relatively easy and quick to set up.