I know an author needs to copyright a book in order to sue anyone who might try to steal it. What about short stories? How does an author protect himself with that type of writing?
You can only sue someone for copyright infringement if you have registered the copyright on that piece. This is true for any type of creative work, including short stories. There are more details here.
Authors of short stories should compile their stories into one manuscript, and then copyright that to save on fees.
Please know that, contrary to popular belief, making a copy of something, and then mailing it to yourself, will not copyright your work.
Easy and affordable copyright registration services are RIGHT HERE.