Everything that is connected to the internet has a unique IP address. Ultimately, the only way you can address a resource is via its IP address. This can be done manually (if you know the IP address of a website, you can access it that way) or automatically. For example if you type in a URL, this will be looked up on a DNS server and translated into the IP address.
So if you want to connect to your computer over the internet, you will need to know the IP address it uses when connecting to the internet. Most domestic internet accounts don't have a fixed IP address, but one that is assigned automatically by their ISP when they connect. To guarantee that you have a the same IP address every time you connect, you need to purchase from your ISP a static address. This will be absolutely unique to you, and therefore will allow access to your machine from anywhere else on the internet.
Once you have your static IP address, you will need to set the router to allow a passthrough of the appropriate port for Terminal services.
Then, when you are running Remote Desktop Client from anywhere on the Internet, you put in the IP address of the computer or router you are trying to contact.