http://wordpress.org/support/topic/twenty-thirteen-footer-question

SEE: the comment by OGC Member.  He explains how to modify the code in the footer.php file located in the Themes – Twenty Thirteen directory.  Only the second line of his example code needs to be inserted and customized.  Remember to backup the original footer.php file before you make your edits.  I recommend that you install and use the app ‘Notepad++’ as your php files editor.  Windows notepad is rather inadequate.

Example:  You can add your owe copyright notice to replace the phrase Proudly Powered by WordPress.