how can I add a “read more” tag directly in the template?

The code would probably be something like this:

echo '<a href="' . get_permalink() . "#more-{$post->ID}\" class=\"more-link\">".__( 'Read more &gt;', 'your-theme' ). '</a>';

Check out the source on how WordPress does it: http://core.trac.wordpress.org/browser/tags/3.3.1/wp-includes/post-template.php#L219

This has to be inside the loop to work and the $post global has to be visible in the current scope.