Don't ask questions while with patients.
Don't ask questions while the doctor is taking notes.
Don't do anything to the patients unless the doctor tells you to.
Do bring a thank you note/card to hand him or her at the end of the experience.
Do ask why they chose their specialty and if they'd do it again.
Do ask for one piece of their best advice about pursuing medicine.
Your role there as far as patients goes will be very limited and observational in nature, so don't expect to learn much about medical terminology or diseases. You may pick up a few things, but that's not the point of shadowing. You really want to see what different specialties offer and what the physician has to say about the field in general. You'll get to see not if you're right for medicine, but if medicine is right for you.