Turn off the power to the light fixture at the circuit breaker. Let the light cool, if it was on. Remove the light bulb and the glass or plastic bulb cover.
Unscrew the light fixture mounting plate. Twist off the two wire nuts to loosen the wire connections. Set the old light aside and unscrew the mounting bracket, if your new fixture comes with a new one.
Place the new mounting bracket over the fixture hole, pulling the connection wires through the hole in the middle of the bracket. Screw the bracket in place.
Connect the white wire of the new fixture to the white connection wire by touching the exposed copper at the ends of both wires and twisting them together. Do the same with the two black wires and the ground wires.
Cover the connections with a wire nut. Twist the nut into place.
Push the wires and the wire nuts through the hole in the mounting bracket and back behind the wall. Raise the new fixture into place and screw it into position.
Install a new light bulb. Push the bulb cover into place. Turn on the power at the circuit breaker.