You will need to pick up a screw extractor at your local hardware store. Look at the packaging and make sure you have a good metal drill bit the size that is recommended for the pilot hole. You want a screw extractor that has a tip smaller than the diameter of the bolt you are removing.
You can purchase a handle designed to be used with the screw extractor or just use an adjustable wrench or a locking pliers to remove the broken bolt. Do not use a drill on the extractor, remove the bolt by hand.
Sometimes you need to tap the extractor into the broken bolt pretty hard to get a good grip. You can also tap the top of the extractor as you are turning it to get a grip.
If you have an old rusted bolt that is broken off, soaking it first with a good lubricant can help.