As far as I am aware, Windows Vista already comes with Remote Desktop Utility (forgive me if my translation is incorrect, but something along those lines) and it is quite easy to set up. You give it the target computer (by IP or URL) and if the target requires more information that is given in the settings. Basically if this is a university of school, anything that requires you to set up a remote desktop, they ought to have a guide on how to set up Remote Desktop Utility so that it works. Catch here is that it does not allow you to remote access computers outside your LAN. For that you need a VPN connection.
Not sure about Windows XP or 7, sorry. There's plenty of programs that are usable though. VPN Client for instance. I haven't had the need to use it for a while so I cannot explain how it is used.