Yes; the cheapest way is to buy a crossover Ethernet cable and connect your laptop to the desktop, then change some settings.
If you have more then 2 computers to share the one broadband subscription, you will need to set up a proper network, which will require the purchase of a router.
Your laptop probably has wireless capability. Wireless routers are pretty much the same price as non-wireless routers so if you want to go the full networking route, thats probably the way to go.
Let us know which would be your preference and we can take it on from there.