First, just as some heads up information. There are two types of RJ connections you should be familiar with, a RJ-11 and a RJ-45. The RJ-11 is a connection used for phone lines and modems, where the RJ-45 is used for Ethernet (network cables) and the RJ-11 is a little smaller in size then the RJ-45.
First, make sure you're connecting a Ethernet cable (not a phone cable) to your laptop. Not all laptops and desktops have a network connection (RJ-45) but may have a RJ-11.
If you're sure this is a network connection and you're using a network cable you're going to need to connect to the laptop, the other end would connect to a network router, switch, or hub. Other computers would then connect into one of these to allow you to play games with other computers on the same network.
If you're trying to go computer to computer you would need a special ethernet network cable called a crossover cable.
A good place to start with networking information is:
http://www.computerhope.com/help/nic.htmAlso searching on Computer Hope for almost any computer definition will give you a definition for that term and also a better understanding with what you're dealing with.
Hope this helps.