Most home routers have a feature called port forwarding. remote desktop by default uses 3389 so you would log into your home router (linksys, netgear, etc..) go into the settings page and look for port forwarding, it is different on different routers. You would forward port 3389 to your home PC that you want to remote desktop to. You then need to grab the external IP of your router which would be the IP given to the router by your cable modem. This again should be in the router interface. Once you setup port forwarding and have the ip, you would open remote desktop on your surface, enter the external IP, you should then see your desktop show up. You then enter your credentials to get in.
Note:
You need a password on your home PC
When you log in, use the format machineName\username in the name column unless you have a domain
To log into your router interface to change settings, open your PC or surface, go to the command prompt and type ipconfig, this will give you your current IP. The default gateway should be the IP of your router. For example, if your pc is 192.168.1.100, your default gateway is most lilely 192.168.1.1 which is the ip of your router. So with that knowledge, open internet explorer and enter
http://192.168.1.1 to get to the login page of your router. Enter the password and away you go.