Shut off the power to the overhead light fixture.
Remove the light bulb from the fixture. Unscrew the base of the fixture with a screwdriver.
Unscrew the wire nuts that connect the ceiling wires with the overhead lighting wires. Set the wire nuts aside. Lower the overhead light fixture from the electrical box and set aside.
Inspect the light fixture to see if there are any obvious problems with it. Check for frayed wires and burned out light bulbs. In many cases it is easier, safer and cheaper to replace the light fixture with new overhead lighting.
Screw the mounting bracket of the light fixture in place.
Twist the metal ends of the wires in the light fixture with the wires in the electrical box. Match together the two white wires, two black wires and green or bare ground wires. Screw a wire nut over the exposed ends of the wire pairs.
Screw the overhead lighting in place with a screwdriver. Place new light bulbs into the fixture.
Turn on the power to the overhead lighting.