Here's how they work, this from straightdope.com. No demons, gods or angels involved:
What makes the pointer move? An effect similar to that which occurs in dowsing, known as the ideomotor effect. This is a fancy name for involuntary/unconscious movement, such as a dowser's hand flicking enough to move his stick when he passes over an area he knows has water. (In fact, Cecil has discussed this very subject.) The basic point is that your muscles can move without your consciously thinking, "move to the word YES." As the Skeptic''s Dictionary says, "suggestions can be made to the mind by others or by observations. Those suggestions can influence the mind and affect motor behavior. What is purely physiological, however, appears to some to be paranormal." In other words, if you believe this stuff and are trying to get the spirits to answer questions proving that they are all-knowing, and you ask a question that you already know the answer to (for example, "What's my father's name?"), odds are that your own hands will do the rest by spelling out your answer. That's where trying it blindfolded comes in (provided you haven't memorized the board, obviously). If it's spirits, they should be able to guide your hands no matter whether you can see or not. But if it's you doing it unconsciously, the blindfold will screw things up.