Copyrighting your work isn't as complicated as it might seem at first. You can decide to rely on your previous drafts (a printed or electronic history that shows the work was created by you), or you can submit your work to the Copyright Office at the Library of Congress.
As the Copyright Alliance states on their very clear worksheet, "As soon as the idea for your novel, poem, or manuscript is written down in a fixed copy, the work automatically has copyright protection. Though registration with the U.S. Copyright Office is not necessary for your written work to be protected by copyright, there are a number of benefits to registering your work," and the worksheet continues to outline what those benefits are. For more information, visit the U.S. Copyright Office (a department of the Library of Congress), and their Factsheets.
Especially for poets, the Poetry Foundation has put together information on fair use in poetry (using work created by other people in your poetry.) The U.S. Copyright Office's Circulars are helpful, including one on how to investigate the copyright status of a work.