When I made mine many years ago, I didn't have a lathe. What I did was to take a piece of 5/16" rod, file about 1 1/2" flat on both sides, ending up with something resembling a really long narrow breech-plug scraper. I then split the flat portion in two with a hacksaw, bent the two sides out and away from each other, and filed them round.
I managed to break the first couple trying to get the spiral by cold-forming them, so don't do that. It was really easy to heat them with just a propane torch, though, and bend the tines around a mandrel with a pair of pliers. I used a 1/4" piece of rod as a mandrel, with the end filed down like a really blunt screwdriver so it would slip down between the base of the tines.
I filed the shank to shape free-hand and drilled and tapped it for a 8-32 screw, then soldered a piece of a bolt in the hole to give me male threads. If you have a lathe you could make the worm in a single piece, but I imagine you would want to any turning before forming the tines.
I used mild steel for mine, but a recent thread here on the subject suggests that some sort of hardenable steel would be preferable, as the tines are prone to deforming in use, particularly when new. They work harden over time, but hardening and tempering to a spring temper would save some aggravation.