How do I remove a broken off light bulb from its base???

First turn off the circuit breaker. Check to make sure there is no power coming through the fixture. Also turn off the power at the switch. Use tweezers, grab the metal part of the bulb, then twist it in the direction to unscrew it. If tweezers do not hold it strongly enough, use pointed pliers but not cutting pliers. Next, put in a new bulb of a lower wattage. Your bulbs will burst if they are too high wattage for the fixture.