Umm... first you need to register a domain, and have it point to the IP address of the box on which you are runnin
tomcat.
If you're only running an intranet site, then you can get away with entering your domain into your internal DNS, and then it won't matter if the rest of the world doesn't see it.
To get Tomcat to respond to port 80 (the default, so that you won't need to type :80) is set in server.xml. Just search in that file for the current port (8080) and replace it with 80.
If you want it to respond to a certain 'named host', then configure a Host with that name, also in server.xml. I believe Tomcat needs a 'default' Host, so you will need at least two host entries now.