How does a water well pump work?

Answer 1

There are several different types. All use an electric motor to turn the pump and move the water.

In all cases the pump has to be able to lift the water to the needed height from the well to the point of use and it has to deliver sufficient volume to be useful.

The specifics of how each pump works is too detailed to write herein. Go to "How Stuff Works" and it discusses this.