I've been using FM screening in presswork since 1970 (kindergartens were very sophisticated back then :-)). This was way before PhotoShop, personal computers, and digital workflows. The method I used was fairly simple, but difficult to perfect.
I would take a conventional low contrast 35mm black and white (or color slide) positive image.
I would then place the piece of film in my enlarger in the darkroom.
Then I would project the image through a piece of frosted glass that had the frosted side in contact with a piece of lithographic film.Lithographic film does not record grey levels - just black and white. It is the same film that printers use to expose their printing plates.
The rough surface of the frosted side of the glass acted like a digital threshold array and broke the image into a random halftone pattern where the frequency of the dots (and to a lesser extent their size) represented the different grey levels of the original image.The coarseness of the frosted side of the glass determined how coarse the resulting "FM" screen was.
The final result was a piece of negative film that my printer would strip into the the job and use to burn the printing plate.