How to display images in related posts?

That is simple:

<?php
$categories = get_the_category($post->ID);
if ($categories) {
    $category_ids = array();
    foreach($categories as $individual_category) $category_ids[] = $individual_category->term_id;
   $args=array(
    'category__in' => $category_ids,
    'post__not_in' => array($post->ID),
    'showposts'=> 5, // Number of related posts that will be shown.
    'caller_get_posts'=> 1
);
$my_query = new wp_query($args);
if( $my_query->have_posts() ) {
    echo '<h3>Related Posts</h3>';
    echo '<ul>';
    while ($my_query->have_posts()) {
        $my_query->the_post();
    ?>
        <li><a href="https://wordpress.stackexchange.com/questions/62969/<?php the_permalink() ?>"><?php the_title(); ?></a><?php echo catch_that_image() ?></li>
    <?php
    }
    echo '</ul>';
}
}
wp_reset_query(); ?>

In functions.php add this code:

function catch_that_image() {
  global $post, $posts;
  $first_img = '';
  ob_start();
  ob_end_clean();
  $output = preg_match_all('/<img.+src=[\'"]([^\'"]+)[\'"].*>/i', $post->post_content, $matches);
  $first_img = $matches [1] [0];

  if(empty($first_img)){ //Defines a default image
    $first_img = "/images/default.jpg";
  }
  return $first_img;
}

Of course, replace the default image path, and style the output to your needs.

Code taken from: http://www.wprecipes.com/how-to-get-the-first-image-from-the-post-and-display-it