Well basically in most cases you want too use an easy-out.
An easy out is a reverse drill bit, usually what you do is drill a small pilot hole in the bolt, then put in the easy out on a low speed drill, slowly apply pressure too the easy-out and that bolt should back out. Also I recommend heating the bolt with a propane torch or the like too loosten it up even more.
You can get an easy-out at most hardware stores. Its like a grippy reverse drill bit, their should be instructions on the package how too use it, or ask your friendly hardware guy for some tips, its not rocket science, but don't use a drill that works really fast or poweful too back it out, I made that mistake once
