I'd like an explanation of the internal workings of HOW 3-way and 4-way light switches work.?

Question

120-volt resedentials

Answer 1

Here you go you lazy SOB.
http://www.wfu.edu/~matthews/courses/p230/switches.html

Answer 2

A 3 way switch is what is called a C type switch - a toggle between two terminals to connect to a 3rd one. Two switches are required. Power comes into one and is connected to either the A wire or the B wire. Those two wires are connected to the other switch where the load is attached. If the second switch is set to wire with power, the load is ON, if to the other one, it is OFF. Thus either switch can change the power path to provide for ON and OFF.
A four way switch has four terminals with a cross over connection inside. Two wires run from 3 way switches at each end of the circuit to one or more 4 way switches in series in the middle of the circuit. In the 4 way, one toggle position connects A-A and B-B and the other cross connects A-B and B-A. Thus every switch can choose whether to connect its output to a live wire or a dead one, but the 4 way provides the choice to the next switch down the line, so they all can turn off and all can turn on at any time.

Answer 3

As you see from Mike's answer, it's hard to explain without pictures. Also, it's much easier to do an internet search for the answer to a question like this than to try to get an answer on here, where you can't be sure whether the people who answer know what they are talking about.

So the best way is to do an internet search on "household wiring" or "three-way switch."