It all boils down to the router you have in front of your Plex server at home.

Some perform Unplug and Pray (shudder) translations for you, and the Plex server will self-configure the port forwarding. Less headache for the unwashed masses, but also potentially insecure.

If you have a more secure environment, your router will not do this for you automatically and you will need to tell your router to open up (usually port 32400) on your public IP address so external requests can reach your Plex server.

If you need more help, just ask. It would be helpful to know what router you are using.