From what I've seen there's a fairly broad assortment of methods. Some depend on how quick and crude one is willing to be! A couple of my built-from-scratch cameras were designed around using standard filmholders -- the first was
a 4x5, the second
an 8x10. The holders are located by three sides of the "box" and held in against a foam light seal by large rubber bands stretched between pegs on the top and bottom of the camera.
Working with typical double weight printing paper or some sheet films, it's possible to have a curved film plane where the paper snaps in between stops at each side. That assumes one shot per box until a trip to the darkroom or changing bag. In cameras made with cylindrical cans, rolling the paper and inserting it to unwind against the can walls could be enough to keep it in place (generally we're not talking mil spec equipment to be shock and vibration resistant here ...

) One could also just tape the corners to a backing plate -- or even use double-sided tape on the back. Depending on the camera design, one might make a built-in holder by fastening two channels, each made of two strips of metal or plastic (or cardboard even), one wider than the other to a backing plate. The narrower strip would be spaced to just a bit over the paper/film width and the wider strip, mounted on top of that would extend enough to retain the edges of the paper/film.
Somebody here years back had a trick to make a sort of magazine load of multiple sheets but I'm not sure of the details (sounds a bit tricky). And there are various ways to implement roll film cameras, although that gets a little tricky implementing winding knob light seals.
A fair number of folks use a commercial camera and replace the lens with a pinhole to wind up with a fairly well-engineered solution. And of course, there are
pinhole body caps for interchangeable lens cameras, and one could make
a pinhole lens board for press or view cameras to achieve a similar result.
So there's a few -- we'll no doubt soon see some more!