Presimably the two computers will be in the same room. I am alo assuming that your desktop has at least one free expansion slot.
If this is the case, it will cost about £20 to network the two computers. You will need a free network port on the desktop and enough network cable to reach the laptop. If you have a USB broadband connector then you may already have the free network port.
Connect the laptop to the desktop and run Internet Connection Sharing on the desktop.
If you already connect through an ADSL modem router, then you only need the cable.
There are other possible solutions, such as wireless networking, but they will be somewhat more expensive.
Please remember to use appropriate firewall / ani-virus protection.