I am wanting to build a prop of the scene from the exorcist where the girl crawls upside down the staircase. I have the staircase. ...any ideas on how to get a girl prop to come down and then reset back up the stairs?
You're talking about a fairly complex prop that would involve alot of egineering including mechanics, pneumatics, and controls. I'm speculating but just from the way asked this it doesn't sound like you have much experience. If this is the case, you may want to start out with something a little easier.
I don't know about easy, but you could move something down the stairs on some form of chain/line and sprockets/pullys, and doing it so you still had nice stairs the rest of the year would be challenging. And that is just to move something down the stairs. In the Exorcist Megan walks down the stairs on hands and feet, inverted. To accomplish that effect and make it look realistic will be even harder.
If I were to even try that, I would start with a ramp that sits on top of the stairs to give you a smooth surface you attach the mechanics to without damaging the stairs. The simplest I can think of would to put rails on the ramp, build a cart that would roll up and down the rails, then try to find an Megan prop that you could pose the right way. Paint the ramp, rails and cart flat black, dim the lights and it might look pretty good. A wiper motor would probably work well at the top of the stairs, with a line attached to the cart to let it down the ramp and pull it back up. Of course you would need some form of switch to detect when the cart reaches the bottom and top of the stairs, and a prop controller or some other device that could reverse the polarity on the motor so it changes directions when you want. You could also use a timer, or the prop controller to add a delay at the bottom. A prop controller could also turn the lights on when Megan comes down the stairs, and turn the lights off when she gets pulled back up the stairs. Finally, you might consider a motion detector to trigger the whole thing. Next step would be to animate the arms and legs so they simulated the movements.
Anything past this would require a lot of mechanics and or computer animation in my opinion.