What you are wanting to do is called networking.
There are several ways to do it.
Most people use ethernet. If your desktop and laptop have network cards you connect a cable called an ethernet crossover cable which has RJ45 connectors on it for 10BaseT or 100BaseT.
other ways are plip which is slow, or serial which is slower, or maybe usb, I have never used usb. or infared.
Do yourself a favor if you don't have ethernet, and get one.