It's never convenient when a bolt breaks off. Knowing and effective method of extracting the broken bolt makes the job move forward again. There's definitely some skill involved, but once you have the technique it's just like clockwork.
Step 1: Drilling
To get this bolt out you have to drill all the way though the bolt, yes all the way though the bolt!! You have to drill all the way though because you need to weaken the bolt so it can come out. If you don't drill all the way though it wont weaken the bolt and the bolt needs to be weakened, there is a reason it was stuck it the first place!
Step 2: Extracting
Once you have the hole drilled then you can use an extracting tool to spin the bolt out. The Extracting tool has a reverse thread on it so when you put it in the hole and twist it the reverse thread grabs the bolt and spins it out.