With respect to actual emergencies I brief every student as follows
1) In the event of an emergency that requires immediate action I will immediately take control. The student is to take no action so as to avoid the possibility of us acting at cross purposes. I will expect him to handle all radio calls at my direction ( ie make a PAN call now we are landing on runway XX) so that I can concentrate on flying the airplane and dealing with the emergency. I will also expect him to read any emergency checklists I call for.
2) In the event of an emergency that does not require immediate action ( eg alternator flail light on), I will leave the student in control and coach him through the required actions.
I also tell the student that in event of an aircraft abnormality, we both have a veto with respect to continuing the lesson or returning to the airport immediately.