How do I set up remote desktop?

The feature is already installed on your Ubuntu. The "server" can be configured in System/Preferences/Remote Desktop, whereas the "client" is in Applications/Internet/Terminal Server Client.

A blog entry explain this better than I can: http://www.makeuseof.com/tag/ubuntu-remote-desktop-builtin-vnc-compatible-dead-easy/

As far as I can see, none of the answers posted so far actually implement user-based security, they simply allow access to a running X session. This page talks about how to launch the X windows manager (or login handler) over the internet. This way, the only application user gets access to is the login screen, just as they would if they were sitting at the local terminal.