Remote Desktop works in exactly the same way over the Internet as over an internal network. However, when working over the Internet, you must take some extra steps in order to establish a connection:
- The client must know the host's external IP address.
- You must create a tunnel for port 3389 on the host's router.
- The host must have a fixed internal IP address.
- The host's router must direct port 3389 packets to the host's internal IP address.
- The hosts's firewall must allow port 3389 packets.
BTW, "Host" is the machine that is being taken over, often a PC at the work place.
"Client" is your own machine, often the PC at your home.