You have to configure the firewall/router at the other computer's location if you want to access it from your location. It won't just work when both computers are not on the same network. How you go about configuring the firewall is specific to that particular router. Each manufacturer handles it slightly differently although the end result is the same. Essentially you 'punch' some holes in the firewall to allow access from your location through to the computer you wish to control.
Here are some of the things you need to know before you start:
The external IP address at the location of the computer you wish to control
If this is a residential/home location then odds are the external IP address will change over time. All you need do to find what address that location has is to launch any web browser and key in the url whatsmyip.org. You can ask the person at that location to do this for you before you start. Once you have this information you can use ARD's Scanner > Network Address feature to 'target' the computer you wish to control.
Configure the firewall at that location to forward external requests on ports 5900 and 3283 to the internal IP address assigned to the computer you wish to control.
Ideally you should do this first as well as assigning a fixed 'internal' IP address to the computer you wish to control as this too may change over time.
Why do IP addresses change?
ISPs dynamically assign external IP addresses to their residential customers. This is because there are not enough addresses to go around. External IP addresses look something like this: 83.25.241.72. Routers/Firewalls are pre-programmed to dynamically assign IP addresses also. It's done this way to make it easy for most people who don't have the first notion of basic networking principles. Their IP addresses look something like this: 192.168.1.20 or 10.0.0.10. These may be familiar to you? If you've ever looked at the Network Preferences pane you may have seen something very similar? External IP addresses are commonly referred to as WANs or Wide Area Networks (the internet as a whole I guess? Internal IP addresses are generally referred to as LANs or Local Area Networks.
No offence intended and I appreciate some or most of this may be beyond you? But I have tried to simplify and explain this as much as possible in the hope it may help you?
Tony