I start a vnc server on my server by putting the following commands into /etc/rc.local
so it is started at boot, and then just keeps running.
# Start a vnc server for tredegar
su - tred -c "cd /home/tred/ && vncserver :1 -geometry 1024x768 -depth 24" 2>/dev/null &
Note that the server is started as my username, not root's.
Then I can connect to it with vncviewer server:1