install vnc4server

sudo apt-get install vnc4server
or install with Synaptic Package Manager

setup

$ vncserver # run first time, set a password

ubuntu 11.04

$ cat  ${HOME}/.vnc/xstartup
#!/bin/sh

# Uncomment the following two lines for normal desktop:
unset SESSION_MANAGER
. /etc/X11/xinit/xinitrc

[ -x /etc/vnc/xstartup ] && exec /etc/vnc/xstartup
[ -r $HOME/.Xresources ] && xrdb $HOME/.Xresources
xsetroot -solid grey
vncconfig -iconic &

#x-terminal-emulator -geometry 80x24+10+10 -ls -title "$VNCDESKTOP Desktop" &
#x-window-manager &
#exec gonme-seesion &
startx &

ubuntu 12.04

$ cat ~/.vnc/xstartup
#!/bin/sh

# Uncomment the following two lines for normal desktop:
unset SESSION_MANAGER
# exec /etc/X11/xinit/xinitrc

[ -x /etc/vnc/xstartup ] && exec /etc/vnc/xstartup
[ -r $HOME/.Xresources ] && xrdb $HOME/.Xresources
xsetroot -solid grey
vncconfig -iconic &
x-terminal-emulator -geometry 80x24+10+10 -ls -title "$VNCDESKTOP Desktop" &
#x-window-manager &

export DESKTOP_SESSION=ubuntu-2d
export GDMSESSION=ubuntu-2d
export STARTUP="/usr/bin/gnome-session --session=ubuntu-2d"

$STARTUP

kill previous vnc displays

$ ls ~/.vnc

$HOME/.vnc/host:display#.pid

$ vncserver -kill :1

start a vnc display

$ vncserver :1 -geometry 1280x768 -depth 24
$ man vncserver # for more information

Start vncserver automatically

http://superuser.com/questions/147109/automatically-start-vnc-server-on-startup

1. Add the following file as /etc/init.d/vncserver (be sure to modify the USER, GEOMETRY, NAME, etc. to your liking).
2. sudo chmod +x /etc/init.d/vncserver
3. sudo update-rc.d vncserver defaults

/etc/init.d/vncserver

#!/bin/sh -e
### BEGIN INIT INFO
# Provides:          vncserver
# Required-Start:    networking
# Default-Start:     S
# Default-Stop:      0 6
### END INIT INFO

PATH="$PATH:/usr/X11R6/bin/"

# The Username:Group that will run VNC
export USER="mythtv"
#${RUNAS}

# The display that VNC will use
DISPLAY="1"

# Color depth (between 8 and 32)
DEPTH="16"

# The Desktop geometry to use.
#GEOMETRY="<WIDTH>x<HEIGHT>"
#GEOMETRY="800x600"
GEOMETRY="1024x768"
#GEOMETRY="1280x1024"

# The name that the VNC Desktop will have.
NAME="my-vnc-server"

OPTIONS="-name ${NAME} -depth ${DEPTH} -geometry ${GEOMETRY} :${DISPLAY}"

. /lib/lsb/init-functions

case "$1" in
start)
log_action_begin_msg "Starting vncserver for user '${USER}' on localhost:${DISPLAY}"
su ${USER} -c "/usr/bin/vncserver ${OPTIONS}"
;;

stop)
log_action_begin_msg "Stoping vncserver for user '${USER}' on localhost:${DISPLAY}"
su ${USER} -c "/usr/bin/vncserver -kill :${DISPLAY}"
;;

restart)
$0 stop
$0 start
;;
esac

exit 0