Depending on which part of a spark plug is broken, the process of removing it from a cylinder varies. If the insulator is broken but the threads and nut remain, you can usually remove the spark plug using a 5/8-inch socket with 8-inch extension. If the nut has broken off and only the threads remain, the task requires a screw extractor.
If only the insulator has broken off, use a 5/8-inch socket with 8-inch extension and ratchet to unscrew the spark plug from the cylinder. Then, use long-nose pliers or a magnetic reaching tool to grip the remaining part of the spark plug and remove it from the cylinder.
If the nut is broken off or partially broken, use a 3/8-inch drive number 5 screw extractor with a 3/8 drive ratchet and an 8-inch extension. Apply penetrating oil to the plug's threads, and affix the screw extractor to the ratchet and extension. Then, turn the screw extractor counterclockwise with the ratchet. As the screw extractor goes deeper into the broken spark plug, it unscrews the broken spark plug at the same time. Once you have removed the broken spark plug, compare the broken surface of the thread to that of the nut to confirm that no pieces fell into the cylinder. If large pieces fell into the cylinder, remove them with a magnetic pickup or reaching tool.