So you have created a custom option using the Settings API.
Lets say you have created an option called footer-text you can display it in your theme using <?php echo get_option( 'footer-text' ); ?>.
Essentially you are echoing the result that is stored in the wp_options table for the option called footer-text.
It is advised to include some of the code you have done already done, this shows you have attempted something and it makes it easier to answer your question.