Remote Access
This is pretty simple - if you are familiar with setting up port forwarding in your router, you probably won't need any instructions here, just the port numbers. If that's the case, you want to configure the port as 32400.
That port number is in the Remote Access page in Plex settings, easy to access. You can also change the port number on the Remote Access page.
Plex have written (and linked to from the settings page) a guide for setting up remote access. I've taken a glance through it and it looks a little complicated as it tries to cover all bases.
In summary, what you'll need to do is log in to your router - probably going to something like http://192.168.1.254 or http://192.168.0.254. This can vary depending on your router configuration, but there will most likely be details printed on a label on your router.
Once logged in, you'll need to look for port forwarding or game and application sharing. Within this menu, you may have to create an rule for Plex - this will be some details about which port to listen to from the internet and what port this should be directed to - you can set them so they match, or so the router will translate it to a different port number on your local network.
Next, you'll need to apply that rule to a computer - here you'll enter the IP address of the computer your Plex server runs on (or select it from a drop down list in some cases) and then which rule to apply - again, probably selecting the rule you just created from a drop down list.
Some routers will change those steps and you may just enter the IP address of your computer and which ports forward, but it'll be easy to find instructions for your specific router in a google search.
Once it's configured, you should see a green tick in the Remote Access settings page, but you should also be able to access your content either from your internet IP address/URL. Alternatively (and a good choice for secure access) is to go to https://plex.tv/web. This is one of the good reasons for having to set up a free Plex account.
