Does the desktop have an rj45 port?
If it does - and it is already within range of a phone socket - then use this with an Ethernet cable to the router....
....which you will need. Are a cable or ADSL customer? This dictates your choice of either a router or a modem/router.
For the laptop without connectivity, you will need (ideally) a PCMCIA card. If you do not have a TypeII PC card slot, then you will have to settle for a USB wireless adapter instead, which I suggest you install in a driver-only state without the manufacturer's software.
If you are currently using the Windows ICF, you will need to disable it and use a good quality free 3rd-party firewall - such as Kerio - on each client. (Client is the correct term for a PC that is a member of a network group).