Greetings,
Well, since it's likely you don't have your own authoritative DNS server running to be able to direct the connection queries to your TS3 server, you could get yourself a Dynamic DNS (a.k.a. DynDNS or DDNS) service to do the routing from the internet to your server. You can learn more about DynDNS
on Wikipedia here, and a couple of organizations that handle DDNS are noip.com and dyn.com.
Of course, if you aren't interested in receiving connections from the internet, and just on your local LAN (again, not likely, but I served as well and could understand running a LAN party in the barracks, especially between floors), you can read the wiki on
the Hosts file.
HTH. Let us know.