Use Wordpress' Excerpt with a "more" link?

Question

Wordpress' documentation suggests adding the following to functions.php to enable what I want to do:

function new_excerpt_more($post) {
    return '<a href="'. get_permalink($post->ID) . '">' . 'Read the Rest...' . '</a>';
}
add_filter('excerpt_more', 'new_excerpt_more');

As per: http://codex.wordpress.org/Function_Reference/the_excerpt

But when I add this to functions.php, and I attempt to use it, I don't see the more link. Here is how I try to use it:

the_excerpt(__('(more...)'));

I've also tried:

the_excerpt();

---

Update: I've tried the following, but it either returns an error (if no arguments), or it doesn't display any excerpt or anything (if an argument):

function new_excerpt_more($excerpt) {
    $link = get_permalink();
    $title = the_title('','',false);
    $ahref = '<a href="'.$link.'" title="'.$title.'">more...</a>';
    return str_replace('[...]', $ahref, $excerpt);
}
add_filter('wp_trim_excerpt', 'new_excerpt_more');

Answer 1

function new_excerpt_more($output) {
    return $output . '<p><a href="'. get_permalink() . '">' . 'Read the Rest...' . '</a></p>';
}
add_filter('get_the_excerpt', 'new_excerpt_more');

Works with:

<?php the_excerpt(); ?>