I have a PC at home connected to the internet. My friend also has a PC at home connected to the internet. I would like to be able to connect to my friend's PC.
My system IP
My friend's systems IP
How do I proceed?
Well, it depends - are you in the same building? I assume not. The actual IP doesn't matter if you're connecting over a WAN (since you can use the computer name).
You need to allow remote connections (Right click My Computer -> Properties. Remote tab -> and under Remote Desktop, check the box.)
Now, go to something like http://www.whatismyip.com/ to get your external IP.
Using RDP on remote PC, type in the IP and see if he can get in. Enter the name of the computer as your computer name, and enter username / password and domain (if using) or workstation name.
You need to have a password for this to work.
If on same password, then open the RDP (CMD prompt and type mstsc.exe) and just type in the name of your friends computer.
This won't work if you're on home edition of XP.
However, I'd recommend using something like TeamViewer, LogMeIn or GoToMyPc which will work regardless of home or not.