Reasons why you want a DMZ and the benefits it offers.
The general idea is that you put your public faced servers in the "DMZ network" so that you can separate them from your private, trusted network.
The use case is that because your server has a public face, it can be remotely rooted. If that happens, and a malicious party gains access to your server, he should be isolated in the DMZ network and not have direct access to the private hosts (or to a database server for example that would be inside the private network and not on the DMZ).
How to do it:
There are several ways, but the 'book example' is by utilizing two firewalls (of course you can achieve the same result with one firewall and smart configuration, although hardware isolation is nicer). Your main firewall is between internet and the server and the second firewall between the server and the private network. On this second firewall, all access from the server to the private network ideally would be forbiden (of course it would be a statefull firewall so if you initiate a connection from the private network to the server it would work).
So, this is a fairly high level overview of DMZ. If you want more technical details please edit your question accordingly.