Technically your songs and lyrics are protected by copyright as soon as it is created and "fixed" in a tangible form such as a recording, or in the case of lyrics written down.  However proving in a court of law that you created something, in the unlikeley event that you would need to, is a different matter. To fully protect your rights in a court of law it is vitally important to register your work with the U.S. Copyright Office, which is part of the Library of Congress. Having done that, you get a certificate of registration and your work is a matter of public record. Then, if someone ever tries to claim authorship for a composition that you created you have a legally acceptable proof of authenticity that the work is yours.

To register, you need to submit the correct application form, a non-refundable filing fee of $65 for offline registration or $35 for online registration, and a non-returnable copy (or copies) of your work. For forms and more information, contact the U.S. Copyright Office via the mail, online, by phone, or even in person.

The Library of Congress
Copyright Office
101 Independence Ave. S.E.
Washington, D.C. 20559-6000

There is a 24-hours-per-day forms hotline at (202) 707-9100. Once your completed application is accepted it generally takes several months to process.