The camera is a fairly simple piece of equipment. The camera is really just a black box with a piece of film. The camera opens a little hole to expose the film when the user release the shutter. Therefore to take a multiple exposure picture, all a person has to do is to expose the film twice.
On old manual advance cameras, you simply release the film spool and cock the camera again. Then shoot away.
Today's electronic SLR cameras usually have a multiple exposure mode. You set the number of exposures to take on one frame, and the camera will not advance the frame until all exposures have been taken.
Unfortunately, most of today's point-n-shoot cameras automatically advance the frame as soon as the frame has been exposed. The only way to counter this operation is to rewind the film and reload it into the camera and start from frame 1 again.
What if you want to double expose frame 5, but not frame 1 through 4? Simple, expose frame 1 through 4 in the dark. You can do this in a window-less bathroom at night, or get a film loading bag. Just remember to turn off the built-in flash!
What if the camera rolls the entire negative into the film cannister? Use a film leader retriever to get the negative out of the film cannister.