One of the most difficult and yet common mechanical systems is a gear train. A great way to transmit mechanical power from one place to another or to increase or decrease power (torque) or increase or decrease the speed of something.
The problems are always that to make efficient gears needs quite a lot of drawing and mathematical skill as well as the ability to machine complex shapes.
For a lot of amateur work it isn't necessary to have maximum efficiency and therefore we can get away with a much easier to make, even with hand tools, system.
A gear is basically a series of teeth on a wheel.
provides a very good explanation of how gears work and how to work out gear ratios.
(Note in the diagram above they have labeled an incorrect number of teeth on the gears - sorry)