Warren in Lancaster, PA
I have made screws to replace broken ones, so I have a sample in hand. I make a strip of paper of the appropriate width and wrap it around the shaft of the new screw. Then I make a pencil or knife line spiraling around the shaft following the strip. This line represents the top of the ridge or the center of the ridge for the screw. Most threads are somewhat flat topped for durability.

Next I cut a groove between the lines with a v (parting) tool. Alternatively I have cut a shallow kerf here with a backsaw. Then using a wide chisel I enlarge the V by paring down the slope of the thread. If the screw is secured, you can pare the same portion of every thread before turning the screw. Your eye can pick up small irregularities in the thread as you carve. I sometimes put the screw on the pole lathe and us a very fine file to smooth things out. This can be done on any lathe at very slow speeds.