I run a desktop and from 1-3 laptops on a 1Mb connection without any problems.
The next question is 'how are you connected to Broadband? Is it a USB ADSL Modem or a more sophisticated Router (this will have more connections on the back).
Does your laptop have WiFi as standard? If it does then that may be the easiest route. However you could connect by LAN cable if the laptop is close to the desktop.
You may need to buy a combined WiFi Router ADSL Modem depending upon your current equipment.
I use the latter with all the PC's wirelessly connected (incl the desktop) as mine are all well away from the Broadband connection.