This is a set of screw extractors/easyout's. Your success with these extractors depends on a few factors but in some instances they will work. Screw extractors have a left hand thread on them, so when turned anti-clockwise they grip the bolt and remove it.

Here we have a sheared bolt in the end of a shaft. Try and get the end of the bolt as flat as possible by either filing it or grinding it flat.

Centre punch the middle of the bolt as this will stop the drill bit from wandering.

Now drill a hole in the dead centre of the bolt. The hole size depends on the size of the screw extractor. You should always use the largest screw extractor that you can, but the drilled hole needs to be smaller than the screw extractor for it to bite.

This is the screw extractor that we will be using, the hole drilled in the bolt is slightly smaller than the size of the screw extractor. Push the extractor into the hole and tap with an hammer.

Using a suitable wrench turn the screw extractor anti-clockwise and if you are lucky the broken bolt will be removed. Be extremely careful as a broken screw extractor or drill bit is even more difficult to remove.