Fixing your music in a "tangible" form asserts copyright. This means either writing down the score or, more commonly, burning a CD of the recording, if you already made a sound recording. Date and title the music, either by writing on the CD or on the score. Make multiple copies of either version and put a copyright notice on all copies. The recording doesn't need to be high-quality, just sufficiently audible to discern melody and lyrics. You could even use the "Voice Memo" or "Dictaphone" function on your cell phone to make the sound recording if you don't have recording facilities.
This is not an official way of registering copyright, but it can prove the existence of a sound recording on a certain date. By sending the recording by certified mail to yourself or a lawyer, you have an official document that includes the date of postage. This document corresponds to a code that appears on the shipping label on the package. So provided you don't open the package, this acts as proof that the sound recording existed prior to the date on the label. This method does not officially register the copyright, however, and is not a substitute for registering copyright. But it does act as evidence that your music had been created before a certain date. In cases in which you need to prove that your work has been copied, you first need to provide evidence of when your work was created.
Send an attachment of the song to yourself or to a friend. Even better, if you have a lawyer, send the attachment to her. Instruct the recipient to download the attachment to his hard drive and to create a backup copy on disc. This approach affords you the same protection as mailing the song. It is not an official copyright registration, but it is evidence that the song existed in tangible form prior to a certain date, as emails are time-stamped.
The only way to officially record a copyright is by registering with the Copyright Office at the Library of Congress. You can download all of the relevant paperwork from www.Copyright.gov, which you send by certified mail back to the Copyright Office, or you can file electronically. The latter method is cheapest and quickest. As of April 2011 it cost $35 to register a basic claim of authorship.