Dead bolts jam for a variety of reasons. The bolt may stick in the strike plate if it is not aligned properly. A variety of parts inside the lock may jam or become disengaged, resulting in stuck bolts. Several steps are required to fix this issue. Once you locate the source of the problem, employ one of these methods to dislodge the bolt.
Lubricate the lock. Spray graphite into the lock. Re-insert the key and twist it back and forth in the lock to free the dead bolt.
Tap the lock with a small hammer or the end of a screwdriver while you turn the key. This may free up the parts inside the lock and cause stuck parts to wiggle free. Try this method several times until the dead bolt slides back into the lock.
Take the lock apart. Unscrew the screws along the side of the dead bolt and slide them out. Pull the back of the lock off of the door. Inspect the inner dead bolt rod and make sure it lines up with the slot inside the lock. Position the rod so it fits in correctly and slide it back in place. Tighten the screws and try the lock again.
Open the door after the dead bolt is freed. With a metal file, file down the inner strike plate to open it up a little more. This will allow the dead bolt to slide more freely in place once closed again.
Repairing locks is a complicated task, so if you have limited skills, hiring a professional is probably your best option.