How does PLANEPUTT putting trainer work?

The 2 inner rails are set at your putter’s shaft angle or plane at address. The shaft stays in contact with both rails to ensure the plane line is not changing angle during the stroke becoming steeper or flatter. The 2 rails ensure the path the shaft takes is truly along a straight plane line.

What’s the third rail for?
The third rail is adjustable to give a clearance gap so practice can be done to not hit any rails. To keep the shaft on both inner rails requires a slight inner force towards you to maintain contact. Trouble is when you are not on the trainer that trained force will direct the putter inside. Practice must also be done to guide through the rails to eliminate this force. It is also true feedback that your stroke is sound. Practice 10 strokes between a set gap. If you get all 10 without touching a rail reduce the gap and try again. If success falls to below 8 then increase the gap. Your goal is to be happy with 8/10.

How do i know what the face is supposed to look like as it moves back and through?
The alignment laser attaches to your putter shaft and projects a line square to the face. Take accuracy in aiming this laser line and align it through the sweetspot of the putter. As you move the putter back and through the laser line must stay parallel or on the TARGET LINE. You will instantly notice any errors in the putter face alignment. Practice keeping the laser line staight or parallel to the target line and then the Face is always square to the Path or Plane as they are both now one and the same. Remember that the putter head and face will “appear” to move inside the target line and open up slightly on the back swing and then move inside and closed slightly on the follow through. This is just an optical illusion as they are both travelling square to the plane.