So you want to copyright your poem about your cat...

If we've established that your work is good enough that people will show interest in it and you might be able to make some money, then congratulations! You're ready for copyright!
A copyright, as defined by the US Copyright Office, is "a form of protection grounded in the U.S. Constitution and granted by law for original works of authorship fixed in a tangible medium of expression. Copyright covers both published and unpublished works" and it protects the original work of the person who created it.
With copyright, you can make copies of your own work and edit it and it protects you from people who want to make derivitives of it (I'm looking at you, Shepard Fairey).
In order to copyright your work, you can go to the US Copyright Office's website and fill out a form. All you have to do is pay a small fee and voilà! Copyright achieved. Good luck!