For some reason, gear cutting was one of the motivations for getting my own machine tools. I wanted to be able to do homemade gears. To be honest, nearly all the gears I have used have been bought or recovered. Nevertheless, it was an itch that needed scratching.
I guess there are three or four likely ways you can go about the process.
Single Tooth Gear Cutting
First, you can cut each tooth, one at a time. Actually of course, you cut the spaces between the teeth. To do this you need a cutter and some way of accurately indexing the gear blank for the cutting. The cutter can be home made or commercial. Commercial cutters for gear cutting are not cheap and you need quite a few to cover a range of different gear sizes and types. Typically, a set of eight are needed for a complete range of gear sizes for a given pitch and pressure angle. This quickly gets expensive. Alternatively, you could make your own cutter my any of the several means described in detail elsewhere (see the links). Home made cutters can be ground for just one size of gear and, like the commercial cutters, will also cut a range of gears of similar sizes.
Second, you could hob the gear. Strictly, this requires a special cutter and a machine whose function in life is to hob gears. The cutter is a bit like an overgrown tap and one hob can generate the correct involute form for gears of any number of teth for a given pitch and pressure angle. To do this, the gear blank must rotate as a specified speed as the hob does the cutting. The ratio of the cutter RPM and the blank RPM determines the number of teth. Hobbing machines are complex, expensive and have awkward limitations for cutting gears with prime numbers of teeth. Free hobbing allows the gear blank to be driven around by the hob. This can result in the wrong number of teth being generated.
A third method is to use a shaper with a single point cutter to cut/generate the teth. At its simplest this is like using a single point cutter as in method one above. specialist gear shapers move the cutter as the gear blank is rotated to generate a correct involute.
Homemade simple gear cutter
The way I chose to do it is a mixture of method one and two. A cutter is made that looks a bit like a hob bit without the helical teeth that require constant rotation of the gear blank. The teeth (or gaps) are cut one at a time with an indexing device of some form. One advantage of this method is that, while the hob has to be carefully made, it does not have to be the exact shape of the gap between teeth. Instead it is a rack form an the gaps each side of the current gap are modified as the current gap is being cut. Better still, a single cutter can be used for gear cutting of any size gear of a given pitch and pressure angle.
The links at the side will give you more details. If you find any errors please tell me so that I can fix them
If you want to find out more about other methods for cutting gears, check out the definitive small work shop guide:
Gears and Gear Gutting (Workshop Practice) from Ivan Law.