You own the copyright to any creative, original work you’ve completed. As the copyright owner of your work, you’re automatically entitled to the full menu of exclusive rights you have in your work.
That being said, you can also choose to register your copyright to gain additional protections. If you believe someone has infringed on your work and you decide to bring a lawsuit against them, you must have registered your copyright to do so. By registering your copyright, you also increase the likelihood that a court would find your copyright claims to be legitimate. And if you win, you’d be eligible for a greater number of legal remedies.
Copyrights are registered with the U.S. Copyright Office. If you’re interested in the process, you can find the details here.