Turn off the power supply for the Kenmore #564-8878310 microwave at the circuit breaker box. Never attempt to service the microwave before removing the power source.
Open the microwave door, remove the retaining screws from the vent cover using a Phillips screwdriver and pull the cover away from the microwave. Locate the bulb holder. It is above the door near the center.
Remove the retaining screw using a Phillips screwdriver and pull the holder straight up. Put on the gloves and remove the old bulb from the holder. Replace the bulb holder into the slot in the microwave.
Install the retaining screw using a Phillips screwdriver, taking care not to overtighten it. Place the vent cover on the microwave and install the retaining screws using a Phillips screwdriver.
Place a cup of water in the Kenmore microwave. Turn the power back on for the microwave at the breaker box. Turn the microwave on and run it for a few seconds to check that the new light is working properly.