There are several ways of extracting a broken bolt, but if there is enough of a broken bolt shaft extending from the housing, the best way to remove it is using a pair of locking pliers to grab the shaft and unscrew it from the threads. If the bolt does not turn, applying heat with a propane torch helps break it free. For bolts that do not extend beyond the housing, using an extraction kit and drill are options.
Using the extraction kit requires drilling a hole in the center of the bolt. Because the bolt does not break evenly, the process requires drilling a pilot hole that guides the larger drill bit. After drilling the hole, insert the extraction bit into place and tap it with a hammer. Use the bit handle or an adjustable wrench to turn the tool counter clockwise. The tool has threads that tighten into the broken bolt as it turns.
Some broken bolts are so seized the extraction tool cannot remove them. In these cases, the option is drilling out the bolt and rethreading the hole. In some instances, rethreading with a tap and using a larger bolt is an option. If the bolt must remain the same size, drill it out and insert a Helicoil kit. This kit screws into the hole and provides the proper sized threads for using the same size bolt.