If you want to add and display breadcrumbs navigation into the wordpress thesis theme, you can do it simply using wordpress hooks.
Look at the following function it will generate the breadcrumbs navigation.The call to it using thesis_hook_after_header wordpress thesis hook.

function thesis_breadcrumbs() {
	echo '
';
		if ((!is_home()) || (!is_front_page())) {
			// home page link/site name
			echo '';
			bloginfo('name');
			echo "";
		}
		// category and posts
		if (is_category() || is_single()) {
			echo "  »  ";
			the_category(' • ');
				if (is_single()) {
					echo "   »   ";
					the_title();
				}
        }
		// pages
		elseif (is_page()) {
            echo "  »  ";
            echo the_title();
		}
		// search page
		elseif (is_search()) {
            echo "  »  Search Results for... ";
			echo '"';
			echo the_search_query();
			echo '"';
        }
    echo '
';
} // end the function

How to display breadcrumb

add_action('thesis_hook_after_header','thesis_breadcrumbs');

Full code is here

function thesis_breadcrumbs() {
	echo '
';
		if ((!is_home()) || (!is_front_page())) {
			// home page link/site name
			echo '';
			bloginfo('name');
			echo "";
		}
		// category and posts
		if (is_category() || is_single()) {
			echo "  »  ";
			the_category(' • ');
				if (is_single()) {
					echo "   »   ";
					the_title();
				}
        }
		// pages
		elseif (is_page()) {
            echo "  »  ";
            echo the_title();
		}
		// search page
		elseif (is_search()) {
            echo "  »  Search Results for... ";
			echo '"';
			echo the_search_query();
			echo '"';
        }
    echo '
';
} // end the function
// call to the function
add_action('thesis_hook_after_header','thesis_breadcrumbs');