How do I remove a broken bulb from the fixture?

I've heard that you can cut a potato in half and push it on the broken end of the bulb and turn it that way but I've not tried it. If it is completely smooth, no glass left you might have to distort the metal that is left so the potatoe can get a grip. Hope it works

Great! I will try that. Thank you!

Shut the power then cut a potato in half and use that

The potato trick usually works. Be sure to cut the power as Kathy said and **be sure to wear wrap-around eye protection** in case there are slivers of glass or flecks of metal flying about. Also before replacing the bulb with the power still off, dry out the socket to be sure there is no potato "juice" or wetness in there. Finally if this doesn't work, you may be able to grab the metal part with narrow needlenose pliers enough to start it unscrewing. You can then hand unscrew it wearing gloves, all done with the power off, of course.

Any chance you have a pair of those safety cutting gloves designed for working with knives or food mandolins...or perhaps heavy duty leather work gloves?

I have removed a broken bulb screw base with pliers. I tried to pinch an edge of the metal rim and spin/jiggle it around but couldn't grab a good bite. I had to bend the metal cup to get a better grip and eventually it became a mission to "crush it til it's small enough to pull out of the socket". It worked but there was no finesse.

I didn't take any chances and cut the power at the breaker. (This fixture was in an older home on a funky three way switch). I also used a thick wad of paper towels to break off all the remaining glass so it wouldn't fall down on me while I was working.

I have used needle-nosed pliers to grip onto the bulb base. Power off at switch. Ensure you are turning in the proper direction. The pliers can bend the metal and potentially break the bond in the socket.