I thought I could just unplug my ethernet connection from my PC and connec it to my laptop and I would be able to get internet connection. This does not work. What do I need to do beforehand to get this to work?
cable modems often are tied into the mac address of the computer that sets them up. You can call the cable company and ask them if they do that - it's a pretty common practice, but generally only with cable. If that's the case, only your desktop can use the connection.
The way around it (if this is what's happening) is to get a router that can spoof the mac address of your desktop. The advantage to the router is that both the laptop on the desktop can be online at the same time.
You might want to look into wireless while you're at it.