Paul M replied: "Step 1: Turn off the breaker to the socket, or at least turn off the switch on the wall
Step 2: Cut open a raw potato and use the open end to push in and turn the broken base out
Step 3: Consider replacing the fixture itself or the bulbs in your house. Although this problem is somewhat common, sometimes it can indicate defective fixtures or bulbs.
With fixtures, it might be an overly tight fit for your common bulbs, or you might have a batch of poorly manufactured bulbs.
Many people are starting to use lubricants on their bulbs to avoid this from happening. Here is an example: "