Assign classes to Custom fields

I think you have to output these Custom Fields manually to do it.

You can do it like so (let’s assume your custom fields are: first-meta-key, second-meta-key, third-meta-key and you set them single value – no field has multiple values assigned to it):

<ul>
  <li><span class="first-post-meta-key">Name: </span> <?php echo esc_html(get_post_meta($post->ID, 'first-meta-key', true)); ?></li>
  <li><span class="second-post-meta-key">Name: </span> <?php echo esc_html(get_post_meta($post->ID, 'second-meta-key', true)); ?></li>
  <li><span class="third-post-meta-key">Name: </span> <?php echo esc_html(get_post_meta($post->ID, 'third-meta-key', true)); ?></li>
</ul>

Another way would be:

<?php $custom_fields = get_post_custom($post->ID); ?>
<ul>
<?php foreach ( $custom_fields as $key=>$values ): ?>
    <?php foreach ( $my_custom_field as $key => $value ): ?>
        <li><span class="<?php echo esc_attr($key); ?><?php echo esc_html($key); ?></span><?php echo esc_html($value); ?></li>;
    <?php endforeach; ?>
<?php endforeach; ?>

PS. It’s not tested (and written directly in here) so can be a little bit buggy.