OK, here is what you're going to have to do.
First you need to find out the local IP address of the computer you want to connect to. Please go to the computer you want to connect to and find the IP address - To do this go to run > type "cmd.exe" > click "OK" > type "ipconfig" and hit enter. It will say "IP Address" write this down.
Second, you also need the Router's IP address but that can be found multiple ways. Visit here:
http://whatismyipaddress.com/ (if your computer is connected to the router, the routers IP address should show, not your local IP)
Third, you need to access the router's administrative console. This may get a little confusing but you need to look for something called "Port Forwarding."
Now remote desktop uses a port to connect to computers, port 3389. So you need to forward port 3389 to the local IP I had you find before (the IP of the computer you are connecting to). Now that you have done all that, start Remote Desktop, and use your router's IP address that I had you get.
Now remember, there must be a password on the computer you are connecting to.
That should be all!
Let me know if you have any problems following those directions.