Linux – VNC Server which attaches to current session

Use x11vnc, It will attach to a running session and let you share the desktop. If you run it as root to connect to an xdm session, you will need to do some research into Xauth as it can be a bit fiddly to set up.

Edit to add: Karl Runge no longer appears to be maintaining the original x11vnc however development is continuing on github. Or you could do as suggested below by @ivan-talalaev and use x0vncserver.

Another advantage of this server is that it supports alot of the advanced VNC features used by UltraVNC including large bitmap caching and file-transfer.

Run dpkg-reconfigure xserver-xorg as root or via sudo, accept the defaults if you're not sure. Then reboot.

If you could post an error message etc also?