The US Copyright law states that the creator of a work owns the copyright unless it was a "work made for hire". It is not required that you register your copyright with the Library of Congress but it is highly recommended as this affords greater legal protection.
You can find complete information about copyrights, including information on registering your copyright and what that costs at: www.copyright.gov
The actual copyright law is contained in Title 17 of the US Code. Cornell University Law School maintains an online version of the entire US Code. If you're interested in reading the actual copyright law as passed by congress you can find more information here: Cornell University Law School - Legal Information Institute