apt-get install tightvncserver xtightvncviewer
Create a new user:
useradd -c "Tightvnc user" -m -r -s /bin/bash vncuser sudo -iu vncuser bash unset XAUTHORITY vncserver
Create the password and you are done.
Note that 5901 is the default port.
Now, everytime you do:
sudo -iu vncuser bash
vnc server will start as that user. You should never run it as root.