How does common salt speed up the setting of the plaster of Paris?
My guess would be that it absorbs the water in the plaster of paris. Plaster of paris normally has what's called 'water of crystallization' in it. However, it sets too fast with just this, so extra water is added. The salt absorbs that extra water, thereby making it set faster.
Here's a website with details about plaster of paris chemically: http://collections.infocollections.org/ukedu/en/d/Jg16foe/7.4.html
and a book called 'Science in the Real World: A simplified story of how technology using chemistry and physics is used in the real world of industry' has good information on it as well.