For those that don't know wheel studs are what the wheel is held onto the car by. A broken stud can be a real safety nightmare if you don't fix it. They make specialized tools and even pneumatic air guns that do the job but the tools that are actually required to do it your self for free are basic if you know what your doing. Here's a simple way to fix or replace them.
In our case the stud wasn't broken, but we did want to run an extended stud since our project will be running a wide tire for racing and need a little more stud clearance. The steps are the same and pretty easy to do, which should save you some a decent amount of money over going to a repair shop.
First Step - Remove the wheel, If your lug nut on the stud is cross threaded or stripped this may not be a simple task. In this case you'll need to drill out the lug nut using a bi-metal drill bit. If you need to do this be patient and tape off your rim so you don't scratch it up while drilling.
Once the wheel is removed look at the back of the rotor. Rotate the rotor until you can see the head of the broken stud. Next the fun part, using a 5 lb hammer, you'll need to hammer out the stud. A few good smacks should free it up. If the stud is broken flush off at the rotor, use a small punch to act as a prod to push it out.
Next place the new stud in the hole, threads out. It will not seem like it fits once it gets to the nurls(base of the stud). This is supposed to be that way, you need to pull the stud in and seat it. Those nurls are what hold the stud in place to the stud doesn't fall out or free spin when tightening the lug nut down.
To seat the stud, place a washer over the stud against the rotor (this will stop the next step from gouging the rotor hat). Next thread over at least two nuts on the stud and seat them again the washer. You can use your lug nut to do this but I recommend going down to your local home improvement or auto store and picking up some normal nuts, so you don't damage your lug nuts in the process.
With the nuts seated against the rotor, use a 1/2 drive ratchet and deep socket to start tightening the nuts again the rotor. This will pull the new stud in the rotor seating it. You'll need to tighten the nuts until the stub is flush against the rotor like the others. If the rotor turns while your trying to tighten down the nuts. There are two options. First if your have person available they can hold down the brake which will stop the rotor from turning. If your solo you can use a jack stand place at the tip of another stud as a stopper. Just be sure your not on the threads or you could damage another stud while replacing the broken one.
That's it. Easy fix and only a small amount of time and tools required.