How do you extract a broken motorcycle spark plug?

You are dealing with a hard metal (steel) that is broken off in a soft metal (aluminum).

You need to be a little more specific about where it's broken at,

How it got broken,

and what you have tried so far,

I will assume it is broken at the base of the exposed part of the plug.

It should be hollow, Try an easy-out extractor.

You want all the lose material to be removed from the cylinder before you turn the motor.

CLEAN,CLEAN,CLEAN, that's the plan.

If the threads are messed up, You can go to a bolt store, A REAL bolt store not Lary's hardware, and buy a Healy-coil to fix it, Get someone with experience for this part.

Good luck.