NOTE: This is an update from my previous post on sharing the desktop or running a VNC Server. This method works great in Fedora 18.
First install the vino package:
yum install vino
Then click on Activities in the top left corner of the screen.
Next type in "vino" and click on "Desktop Sharing" under Applications or under Settings.
Next click "Allow other users to view your desktop". Make sure "Allow other users to control my desktop" is also check.
The rest of the preferences are up to you. I prefer to uncheck "You must confirm each access to this machine". I also prefer to check "Require the user to enter this password" then enter a password.
I also only prefer to show notifications when someone is actively connecting by selecint "Only when someone is connected" at the bottom.
When done click "Close".
Next you will have to log out of X-windows and Log back in again for the server to start. NOTE: it will only run the server when you are logged in.