You automatically hold the copyright to any original design as soon as you 'publish' it (make it public in any way). You do not have to use the copyright symbol or state that it is copyright protected, but you certainly may if you wish.
In order to legally defend it against copyright infringement (someone using your design for profit or claiming it as their own), it has to be registered. Here's how (it is, however, currently closed, as is the rest of the government, so you cannot register right away).
http://www.copyright.gov/help/faq/faq-register.html
And here's everything (and more) that you ever need to know about copyright.
http://www.copyright.gov/