Like any other countries copyright law that I know of, the copyright law of the USA states that the (initial) copyright of a work vests with the author of the work, with the exception of a work made for hire. You don't have to take any actions to claim it nor have to pay for it (in contrast to concepts like trademarks or patents). You would have to voluntarily transfer it to someone else in order to lose posession of it.
See:
http://copyright.gov/title17/[
^]
Esp.:
http://copyright.gov/title17/92chap2.html[
^]
You may however register your work at a copyright office which
potentially can have some benefits. See:
http://copyright.gov/help/faq/faq-general.html[
^]
I don't take legal liability for this advice.
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