The basic way a pinhole camera works is that light goes through a pinhole (a very small hole in the front of the light-proof container) and hits the photographic paper at the back of the container, which reacts when exposed to light and creates the picture.
So, to apply this to an oatmeal box, get your cylindrical oatmeal can and find the center using a ruler. Cut a square (using a razor/exacto knife/etc- it helps to mark it first with a marker) about 1/2" by 1/2" in the center. Then take some Elmer's glue and glue the seam on the inside of the plastic lid, and around the seams on the bottom of the oatmeal box (this seals all the places where light could leak in). Then, find an aluminum can and cut off the top and bottom, and then cut it lengthwise so it's a flat rectangle. After marking a 2x3" rectangle, cut it out, and round off the corners so you won't cut yourself.
Now, spraypaint the can & lid black (this should be done outside) to make it completely lightproof. Now, take your aluminum rectangle and poke the pinhole in it with a pin (a sewing needle should work fine). Try to only push the tip in, just enough to make a hole- the smaller the hole, the more in focus your photos will be. Then sand both sides of the aluminum around the hole to make it smooth.
Next, take electrical/duct tape and place it on the two long sides of the aluminum. Then put some crazy glue (or just very strong glue) on the area around the pinhole - but NOT covering it!! - and attach the aluminum to the inside of the can, so the pinhole is peeking out of the square hole. This is your pinhole! (We use aluminum for the pinhole because the walls of the oatmeal can are too thick)
You can also make a shutter for it, but covering it with anything thick enough that will keep out all the light when you are not exposing the photo paper will work. Now just put photo paper in your camera and start experimenting!