Wikipedia wrote:
A fully qualified domain name (FQDN), sometimes also referred to as an absolute domain name, is a domain name that specifies its exact location in the tree hierarchy of the Domain Name System (DNS).
http://en.wikipedia.org/wiki/Fully_qual ... omain_name
Simply means mycomputer.mydomain.org instead of mycomputer.
There is much to setup with any OS's network connection. When DHCP is available from your router or systems in place by your network and system admins it's pretty easy on a modern OS - just plugin. Back when these systems were young you needed to provide the IP address for the system, the subnet mask (how much of the network is yours and not behind a router), the default route (router that gets you to the internet or other networks), and if you don't want to use IP addresses to reach everything - the IP address of the DNS server you use.
It sounds like you might need to get comfortable with google for an evening or two on your modern system. You can see your current settings on Mac OS X with the network control panel - be sure to click advanced. Or with the command IPCONFIG /ALL on Windows. Just remember the IP address for every computer in your network needs to be unique. Since you probably have DHCP running on your router you'll want to find a few addresses outside the range it hands out and keep a spreadsheet or notebook to keep static assignments.
I can't tell exactly how much experience you have with networking, I tried not to get too basic, but cover most the keywords if you need to search for more information.
Just looked at the link pentium provided and that should get you going if you know your network well enough to provide all the addresses specific to your network.