Effective bolt extraction separates the real mechanics from the wannabes.
Preface) Make sure you have good drill bits and a clear path to holding the drill bit straight.
1) Center punch the bolt before you start. If it's broken off at a slant, it's gonna be a b!+ch.
2) Start with a 1/8" bit and drill down the center, keeping it absolutely as centered as possible. Going all the way through the bolt is good. Going deeper into the head is not.
3) Drill it out to your extractor size.
4) Set your extractor in the hole. I like to give it a single tap with a small hammer to help set it, some people don't.
5) Using firm downward pressure, start turning the bolt out.
6) Watch the extractor and bolt. If the extractor starts flexing and the bolt isn't moving, reassess. You REALLY don't want the extractor breaking off in the hole.
7) If it won't come loose, drill the bolt out close to the size of the threads.
8) Try and use a punch to collapse the bolt remnants inward so you can pull them out or use a pick to rotate them out.
9) If you can't get the remnants to collapse, carefully run a tap down the threads. You'll be starting and backing out often to clean out what you can.
10) If you dork up the threads, drill it out one size larger, tap it, and install a helicoil.