The link to KHK Gears

Gears translate motion to a different axis, as well as translate between torque and speed. There is very good and detailed documentation on these parts, so rather than writing an inferior version, I recommend going to https://khkgears.net/new/gear_knowledge/introduction_to_gears/. They have details on different types of gears (https://khkgears.net/new/gear_knowledge/introduction_to_gears/types_of_gears.html) and example applications (https://khkgears.net/new/gear_application.html), among very many other resources.

Somewhat ironically, one thing I will say that the KHK gears will not tell you is to avoid using/applying gears yourself. That is, to use gearboxes whenever possible. Errors in the type of bearing support and shaft alignment are common when doing it manually, and using premade gearboxes avoids these problems. Especially if you just want a gear reduction for a motor, you should use planetary gear boxes that come with VEX motors.