Ok, how did it break (meaning *where*) and what do you have left to work with ? If the head broke off leaving anything more than 1/4" or so of the stud sticking up then I'd suggest trying a set of vice-grips first (do yourself a favor & soak what's left in penetrating oil. Rap it every now & then to set up vibrations allowing the oil to penetrate). If there's enough there to grab onto you can probably use the vice-grips to slowly back it out. If it's broken either flush or below the head then it'll be a bit more difficult. I'd start with trying a small drill bit & an easy-out. Be sure to use a punch to center-punch the broken piece so the drill won't be as likely to wander. Once you have the pilot hole drilled use the smallest easy-out and see if you can't get it to bite & back it out. If *that* doesn't work then you're going to be stuck with outright drilling it out. Use the easy-out hole as a pilot and slowly drill the stud out. Only step up one, maybe two sizes at a time instead of trying to jump right from the pilot to a full-diameter drill. If you're careful and the hole drills true you may be able to save the threads. With 95% of the broken stud drilled out you can often save the hole by running a tap down it but *only* if you remove almost all of the broken stud, don't try it otherwise or you'll wind up with a hardened tap broken off in there and that will ruin your day. If you can't save the threads then you'll have to drill it out oversize & use a heli-coil to repair the threads once it's drilled, either that or retap the hole to the next larger size (sometimes it helps to use an equivalent size metric tap because the threads may be just a hair larger letting you retap to metric without really redrilling it any further, but that's a personal choice). Use a lot of oil or WD-40 to lubricate your drill bits, especially the smaller ones and *go slowly* backing the bit out frequently to clear chips & re-oil, otherwise you risk breaking off part of the bit in the stud and making the job a whole lot harder. Once again, *be careful* trying to drill out the remaining stud with half of a broken drill bit in it will really ruin your weekend, so don't do it.
If you're *very* patient you can use a dremel (or equivalent rotary tool) and a small, skinny stone or better still, a diamond coated burr to carefully grind out the broken stud. I've seen it done & it takes a LOT of patience but it produces good results & saves the threads.
In an absolute worst-case scenario someone will wind up pulling the head off so that the work can be done on a drill press. Do your best to avoid letting that happen. Take it easy, go slowly. Drill carefully & drill straight. *don't* get anxious and jump drill sizes, be patient. This isn't the end of the world but it *does* have the potential to turn into a serious pain in your a$$ if not done slowly & patiently.