I can remote desktop from XP Home to an XP Pro machine (the host has to be XP Pro and it has to have that feature enabled). I do believe I had to download the client software for XP Home from Microsoft.

Like Ed said, the Remote Desktop software needs to find the other computer. On a local Windows network, I can either do either by computer name, or by IP address. On my network, I did it by name, so the address can change according to my router's wishes. As Ed said, across the internet, you will need to use the IP address. I haven't played in that area, so I'm not comfortable with that end of things.