If you use light bulbs -- and who doesn't -- sooner or later you're bound to break one, whether by accidentally bumping it or by being heavy-handed in an attempt to remove a blown-out bulb that has become stuck in its socket. There are gadgets on the market with "fingers" that grip broken bulbs and allow you to unscrew them. However, you'll save money and a trip to the home-improvement store with a tried-and-true manual method of removing a broken, stuck bulb.
Unplug the lamp with the broken bulb, if that is where the broken bulb is. Cut power to a light fixture at your electrical box. Find the switch for the room where the fixture is and flip it to the "Off" position. Test an outlet in the room to make sure the power is, in fact, off.
Spread newspaper below the light fixture or lamp that has the broken bulb to catch glass fragments.
Put on the work gloves and goggles.
Press the bar of soap into the broken glass fragments, if any remain in the bulb. Embed the fragments as deeply into the soap as possible, being careful not to cut your hands.
Twist the soap clockwise, slowly but firmly, to unscrew the bulb from the socket. If the glass breaks, you'll need the pliers to continue.
Grasp the edge of the bulb's metal base. Bend the base in slightly, if necessary, in order to get a grip with the pliers, but take care to not break it.
Rotate the bulb base counterclockwise in the socket. Budge it clockwise in order to wiggle it a bit if you're not able to move it at first, and then try again to rotate it counterclockwise.
Replace the broken bulb with a fresh one.
Restore power to the fixture or lamp.
A potato can be substituted for a bar of soap when removing a bulb with glass fragments. Blow dust and dirt from around the threads of the bulb base if it is preventing the base from rotating.
Never assume electrical power is off. Always test it to be sure.