Turn the fixture's power off at the wall. Remove any shades or fittings attached to the light socket. Remove the screws from around the edges of the socket itself and gently lower the socket from its fixture. Remove the insulating sleeve from inside the socket.
Attach the clip of the continuity tester to the hot lead, which is the brass screw terminal or black wire lead, in the front of the socket. Touch the probe to the tab or screw it into the base of the socket. If the continuity tester does not glow, the socket itself is faulty.
Attach the continuity tester's wire to the neutral lead, which is marked by a white wire or silver screw. Touch the probe anywhere in the threaded portion of the socket. If the continuity tester does not glow, the light socket is faulty and must be replaced.