Simple DC motor with one bar magnet https://www.instructables.com/id/The-Simple-DC-Motor/ 
I'm struggling to get my head around how this motor works.
Let's say for the sake of argument that the field lines are running from the LHS of the bar magnet round to the right and that current flows through the coil in a CW direction. 
In the bottom right of the coil this would give us a force out of the page. but as the current travels round to the bottom left side of the coil it now has a vertical upward component and the force would be in to the page. 
What am I missing?
 A: You are missing the fact that this simple motor has a commutator which does not allow current to flow during half a revolution of the coil so the direction of the force/torque is never reversed it just goes from being in one direction to zero to being in the same direction as before to zero etc.  
 

Hold the loop vertically by placing your thumb through the center of the rotor Place one
  of the straight sections of wire on a flat surface. Using a razor blade, strip ONLY the
  TOP surface of the wire. Be sure not to strip the sides or the bottom, just the top. Strip
  the wire from the coil all the way to the end of the straight section  

is the first instruction which enables the current to the coil to be switched on and off during one revolution.  

The other important feature of this motor is that it uses a magnadur magnet which has magnet poles top and bottom as shown in the diagram below.  

A: You are right that if the magnet's field lines run from left to right in the illustration, the coil will not turn.  The type of magnet shown is magnetized in the vertical direction, so that the field lines exit the top and bottom faces.  When a current flows through the coil, the coil roll rotate so that the magnetic field density inside the circle formed by the coil is maximized.
