Some examples on how to customize the read more link in the Genesis framework.

gistfile1.php

<?php

// Add Read More button to blog page and archives
add_filter( 'excerpt_more', 'wsm_add_excerpt_more' );
add_filter( 'get_the_content_more_link', 'wsm_add_excerpt_more' );
add_filter( 'the_content_more_link', 'wsm_add_excerpt_more' );
function wsm_add_excerpt_more( $more ) {
    return '<div class="more-link"><a href="' . get_permalink() . '" rel="nofollow"><span>Read More</span></a></div>';
}

// The three filters should cover most instances when you'd want the Read More link.
// You can comment out the one(s) you don't need.
// Notice that we wraped the link in a div to give more positioning control 
// and the span adds an extra element for styling purposes

// The default Genesis code looks more like this:
    return '<a class="more-link" href="' . get_permalink() . '" rel="nofollow">Read More</a>';
    
// To add elipses just do this:
    return '... <a class="more-link" href="' . get_permalink() . '" rel="nofollow">Read More</a>';
    
// You can also add elipses in the first example with the div, like this:
    return '... <div class="more-link"><a href="' . get_permalink() . '" rel="nofollow"><span>Read More</span></a></div>';