Publishing a web site on internal server

This is probably going to seem like one of those ridiculously easy questions to everybody, but it's something I've never bothered with until now. I need to publish a web site (built by someone else) to a web server on our system. It's already built for internal users, but I don't know how to publish it to the rest of the world.

So it is built on a stand alone server and it's accessible internally through the IP/name

I'd like to make it available to people outside of our LAN as a subdomain of our company domain. name.company.com

How do I go about doing this? Our company name is already registered to us, and we have some sites already published. One is published by a web hosting company and the other is done internally.