If you have some money to spare, get a very cheap and simple camera.  One from a 2nd hand store for two to five dollars is perfect so long as it works.  Show your very young child how to press the picture button, and if it has manual film

advance, how to wind on the film.  Don't show them how to use any other buttons and tell them they are not to touch any other buttons.  That they might break it if they do is a good workable excuse if they want an explaination.  Don't take any particularly valuable photos in doing this and be prepared for the camera and film to accidently end up destroyed - hence why you don't use a good one.  Don't let the child know that there is film inside, don't let them know that the camera can be opened, and very carefully tape-up any buttons that might allow access to the inside of the camera.

Once your child has the idea of how to "play" with the camera,  when they aren't expecting it, secretly put some film in it and leave it laying around in reach of your child.  As soon as you see your child go for the camera, don't say anything, just "ignore" them and see what they do with it.  If they want to take photos of you, then by all means, interact.  Otherwise, just let them go about taking photos of whatever tickles their fancy.  Let them think they are unsupervised and let them try to be sneaky.  This is their time to have some harmless fun.  Of course keep an eye on them, you don't want them pulling the camera apart and eating the contents, or getting hurt trying to take a photo of something they shouldn't be anywhere near.

Check at the end of each night to see if they have used up all the film in the camera.  Once the film is used up, take it out and process it.  You may end up with absolutely nothing, you might end up with something wonderfully amusing or interesting.  My boy at the age of two took photos of the dog's food bowl, the ceiling, the window lock, three views out one window - one of which captured someone walking past, and five he took of himself.