After you determine that a burnt-out bulb is not the issue with your light fixture, and the circuit breaker is still on, use a multimeter to complete three different tests on your light fixture. These tests will determine the exact cause of your fixture's failure. One of these tests must be completed with the electrical power feeding the circuit. If you are uncomfortable with working around live circuits, call a licensed electrician for the live power test.
Remove the light shade from the light fixture. Remove the light bulb to access the screws that hold the fixture canopy to the electrical box. Remove the screws to lower the canopy from the ceiling and access the electrical wiring.
Turn the dial on your multimeter tester to 250 AC to test the circuit for electrical power. Insert one lead into the wire connector holding the black wire from the house circuit to the black wire from the light fixture. Touch the other lead to any metal inside the electrical box. The tester needle or LCD screen registers about 110 to 120 volts if electrical power is reaching the fixture. If you do not receive a reading, call an electrician to trace the wire for damage.
Turn the power off to the circuit at the switch or at the main breaker panel. Turn the dial to Rx1k to test continuity of the socket on the light fixture.
Touch one lead from your multimeter to the terminal that attaches the black wire to the back of the socket. Place the other lead in the socket and touch the contact tab in the socket's bottom. If the meter registers any reading, this part of the socket is good, and you need to test the side of the socket. If the meter does not register a reading, you must replace the socket.
Touch one lead from your multimeter to the terminal that attaches the white wire to the back of the light socket. Insert the other lead into the socket and touch the socket threads. If the meter does not register a reading, you must replace the socket.