How are you connected now? ADSL modem or modem router?
If USB modem then share internet connection with either network crossover cable (both in same room but cheapest option £5 for cable)
wireless adaptors (laptop can be in another room)
wirelss card in desktop (or usb wireless adaptor). wireless adaptor in laptop (if laptop not wireless already).
USB wireless adaptors £20 each just plug in spare port.
These set ups mean desktop has to be on before laptop can connect.
ADSL modem router means laptop can work direct from router even if desktop switched off.
Need router = wireless cards as above