Ensure that your Theme supports Post Thumbnails, and that the client sets a “Featured Image” for each post. Then, combine the_excerpt() with the_post_thumbnail(), e.g. like so:

<?php
if ( have_posts() ) : while ( have_posts() ) : the_post();

    ?>
    <div id="post-<?php the_ID(); ?>" <?php post_class(); ?>>

        <div class="featured-image"><?php the_post_thumbnail(); ?></div>
        <div class="post-excerpt"><?php the_excerpt(); ?></div>

    </div>
    <?php

endwhile; endif;
?>

Then, just use CSS to style according to your needs.