Congress established the Copyright Office in 1897 within Library of Congress.
Copyright Act of 1976 (17 United States Code)
You can register your work with the U.S, Copyright Office, but your work is automatically protected as soon as you create it.
In the United States, copyright lasts for the life of the person who creates a work plus 70 years.
Columbia University's Fair Use Check List provides a tool to analyze fair use. These are only guidelines with the ultimate question being whether the cumulative weight of the factors favors or turns you away from fair use.
How do I register my copyright? You need to submit a complete application form. See Registration Procedures and Circular 4, Copyright Office Fees.