What you require is a wireless router.
You may also need an ethernet adapter for your main PC if it does not have one already.
Different routers are used depending on which type of broadband you have.
For ADSL they are available with built in modems which would replace an existing one connected to the PC via USB. (I`ve not come across any routers with USB connections hence the requirement for an ethernet adapter on your desktop.
Assuming the simplest scenario of a cable modem connected to the PC via ethernet, the router would need the existing cable from the modem plugged into a port marked WAN and a new cable connected from the PC to a port marked LAN (usually several available for more than one wired PC connection).
You would then enter your ISP account details into the routers inbuilt software.
The router will now appear to the cable modem exactly as your PC did running your ISP`s software. It will pass requests from any computers connected to it either, wired or wireless, invisibly and does not require your main computer to be on when the laptop needs internet access.
If you post more details on your current broadband set-up I could be more specific but you probably get the idea.