The process started with finding some hardened steel rod of the appropriate outer diameter. In this case, the screw head will be the largest diameter of the part. I chose some steel rod just a bit bigger than the size of the finished screw head. I chucked the rod into a collet in my lathe. I used an antique American Watch Tool Co. watchmaker's lathe, but any small precision lathe for metal would work. Using a carbide graver, I turned the piece down where the screw threads were to be. Using a graver is something like turning wood on a lathe, but with metal on a very small scale.
Once the threads where cut, I used the graver to start a parting cut. I made the cut in from the end to leave room for what would become the screw's head. Once the placement of the cut was established, I used a Swiss knife-edge file to part away the piece. The file was held with a hand at each end, the end with the handle resting on the lathe tool rest. I did use power to the lathe for this operation.
I did almost everything while wearing a magnifying eye loupe. I didn't realize how small the screw was until I sought out a penny to use in a photograph for scale. The screw works perfectly and cannot be distinguished from the 100 year old screw right beside it on the clock.