Set up an alternate light source in the bathroom. Place a table lamp on a flat surface near the work area where it is out of the way. Connect an extension cord to the lamp, and connect the other end of the cord into a wall outlet outside of the bathroom. Turn on the light switch to the bathroom vanity light.
Turn off the circuit breaker to the bathroom. If the vanity light goes off, you got the correct circuit breaker. Turn on the table lamp, and turn off the light switch to the vanity fixture.
Unscrew the bulbs from the vanity light fixture. Set the bulbs on a towel out of your way. Remove the globes or shades that are attached to the fixture. Most globes have three thumbscrews that secure the globe fixtures. Turn the screws counterclockwise to remove the globes.
Locate the screws securing the fixture to the wall. The screws can be decoratively hidden as protruding buttons that appear to be part of the fixture. Other types have screws that are out of sight along the edge. Remove the screws with a Phillips-head screwdriver, or turn the decorative screws counterclockwise by hand.
Score the edge of the fixture where it meets the wall with a utility knife to remove any natural paint adhesion. Ask a helper to assist with pulling the fixture away from the wall far enough that you can access the wires. Ask your helper to hold the fixture while you disconnect the wires.
Untwist the wire caps securing the vanity fixture wires to the house wires. As you separate the wires, twist a wire cap on each house wire. Pull the fixture away from the wall. If you have a mounting plate on the wall, remove the screws securing the mounting plate and pull the mounting plate off the wall.