If you are using a router, it will share Internet with all computers on your home network. If you don't have a router, you can connect an ethernet crossover cable between the machine with Internet access and the laptop. This requires available network interface cards on both. Then run the network setup wizard on both machines starting with the desktop. Use the same workgroup name on all computers. Enable Internet Connection Sharing and File/Printer sharing.
This will assign a static IP address of to the desktop. The last octet of the laptop IP address will vary with use; 192.168.0.xxx.