All of this assumes a traditional, manually operated lathe.
All the maths can be done using an Excel package called “Hobnail”.
First method – suitable for small helix angles
This takes advantage of the fact that many helical gears can be seen to be part of a screw like thread where the thread does not have straight sides but special ones that mean that two threads will roll over each other.
This way this is done is to make a conventional thread with the helix angle required and a nut to fit it. The end of this is made into an arbor that can be used to hold the workpiece, ie, the uncut gear. The nut is fitted to a block the can be mounted on the cross slide of the lathe. The center height of the screw is at the center height of the lathe. The block can be rotated.
The screw needs some sort of indexing arrangement. this system cuts one tooth at a time. After each tooth has been cut the system is “rewound”, indexing by one tooth spacing and then the next tooth is cut.
(The cutter has to go through the cut backwards without spoiling the cut.)
The cutter is one of the Brown and Sharps type. It is fitted to an arbor and this is fitted and centered in the four jaw chuck mounted on the spindle of the lathe.
The cutter is started and the workpiece is screwed towards the cutter till the length of tooth has been cut. The cutter is turned off and the workpiece is unscrewed. It is indexing round, the cutter is started and the next tooth is cut.
This is very similar to the helical gear copying method I have described for use on the milling machine. One difference is that, that system copies an existing helix. In this case, using a screw, the helix angle is that of the longest screw thread that can be cut, which can be very limited.
for details see “Making helical gears on a milling machine”
Second method – suitable for large helix angles
The workpiece is mounted on an arbor held in a four jaw chuck. A milling spindle holding the cutter is mounted on the cross slide.
The gear ratio is set using the standard gearing for screw cutting. However because the lead is much longer than is required for screws the gear train is the wrong way round. This also means it cannot be driven from the headstock spindle. The drive to the headstock is disengaged. The leadscrew is driven using a handle on the end of the leadscrew.