Last time we explained that in a 3-way switch setup (in which two switches control a single fixture), the switch redirects the current to one of two “hot” wires, both of which proceed to the second switch.
These red and black wires connect to the two corresponding terminals on the second switch. The switch allows the current to proceed from one or the other of these, through the switch’s common terminal to the light.
Here’s an example: If the first switch directs the current to the red wire, and the second switch is switched to allow the red wire to heat the common terminal, the light will be on. If the second switch is switched to allow the black wire to heat the common terminal, the light will be off. And vice versa.
Note that in the diagram, we’ve used the white wire to carry the current from the fixture box to the second switch. You must paint it black to indicate this. (We’ve also left out ground wires to simplify the diagram.)
Naturally this setup will look a little different, depending on where the power source enters the picture (it could also come through the fixture.) Actually though, it doesn’t really change. The current still goes to the common terminal of the first switch first, and proceeds along the same path as in our setup.