I assume there's a lot of skill in assembling as well.
I'm very curious how they made gears etc. say a 100 years ago too considering they're so tiny.
Gears are typically made with a gearcutter, a precision indexing instrument that revolves a 'blank' through all the gear spur positions to cut the gear halves one-by-one from the blank until the whole gear is done. If you're going to use a high quality hardened steel bit for the cutter and a much more mild material (such as brass) for the gears then you should get a lot of stand time out of a cutting bit.
Another technique you might try is etching, which can be used to make quite high precision parts. And if you want to do some minor automation it is fairly easy to see how a bit of knowledge about stepper drivers and basic machining might help you to create a reasonably accurate and quick automated gear cutter.
An off-the-shelf CNC machine that will cut gears for you is possible but one that is precise enough for watchmaking will set you back a small fortune. Making your own tools and toolbits is a good part of the fun of a project like this.
Also etching sounds an interesting approach too.
But you can also saw the profile manually.
Assembling is hard but doable, the hardest part is the adjustment!
That is something I've wondered; until what scale is that really feasible? Because fancy indexing lathes, gear cutters and CNCs bring in kinda high barrier to entry, but a jewelers saw (presumably?) and a vise are far more approachable for a hobbyist.
I don't know about these days.