How do I turn off the laptop screen while using an external monitor?

Find the Name of displays by run xrandr in terminal(your laptop screen is something like LVDS1, and your external monitor is some thing like VGA).

# turn off laptop screen
xrandr --output LVDS1 --off   

If you need to turn on the laptop screen::

# laptop screen on
xrandr --output LVDS --mode 1280x800

If you want to turn off external screen::

xrandr --output VGA --off