It was fairly obvious that the door switch on our Whirlpool dryer had gone out. The dryer hadn't been stopping when the door was opened for a while and the switch had become rickety.
The repair was really simple: just remove the screws holding the control panel and flip it up to remove the screws holding the top to the dryer and slide it off. From there you'll need to take out the two screws holding the door switch to the top left of the dryer and disconnect it from the wires.
The part we ordered worked perfectly. Just do the above steps in reverse to install.