Right when you're trying to remove an old light bulb, it breaks on you, leaving a base stuck inside the socket. Here's how to remove it quickly and safely.
Turn off power to the bulb and unplug the lamp.
Put on protective gloves.
Grip the metal lip of the bulb with needle-nose pliers.
Gently unscrew the bulb base, turning it the same way you would an unbroken bulb. Watch your fingers while turning the bulb base. Sheered glass remnants may still be inside.
Remove the bulb base from the socket.
Be sure to vacuum up any broken glass from the floor.