How to display the user’s comment status on the front end

Displaying comment status is quite standard in every theme; maybe you have not been notice it but you have seen it for sure. All default themes do it and the default wp_list_comments() function does it also and it is the most common function used to display posts comments.

So, if you use default wp_list_comments(), you are displaying comment status already; if you are using a custom callback, you can check the comment status, for example like this:

<?php
if ( '0' == $comment->comment_approved ) {
   ?>

   <p class="comment-awaiting-moderation"><?php _e( 'Your comment is awaiting moderation.' ); ?></p>

   <?php
}

Or more accurately, you can use wp_get_comment_status() function:

// Return 'deleted', 'approved', 'unapproved', 'spam' or false on failure
$status = wp_get_comment_status( $comment_id );