This is a fast and working method, how one can share his desktop session with VNC server on a Linux machine running X.
In this case I did it with openSuSE 12.1, but this should work on all Linux distros running X. Only the way how you install x11vnc may be different of course.
1. Install VNC Server program (x11vnc)
# zypper install x11vnc
2. Create the VNC password (otherwise no password would be required)
# x11vnc -storepasswd
By default, this will create a .vnc folder in your $HOME path, with a file called passwd:
3. Launch VNC server
# x11vnc -forever -rfbauth ~/.vnc/passwd &
And voilà, you can connect to your own desktop with a VNC viewer from a remote computer.
In case you want to share your desktop and want to confirm remote vnc requests, you can ask for a pop up window to appear:
# x11vnc -forever -rfbauth ~/.vnc/passwd -accept "popup" &
The popup will (by default) time out after 120 seconds. This can be set with -accept "popup:N".
See x11vnc --help for more details.