step 1 of customizing comments display

comments.php

<?php 
//hide all of this file if the post if password protected
if( post_password_required() ){
	return;
}

//get a distinct count of comments vs. pings
$comm = get_comments( array(
	'status' => 'approve',
	'post_id' => $id, //This post
) );
$comments_by_type = separate_comments( $comm );
$comment_count = count($comments_by_type['comment']);
$pings_count = count($comments_by_type['pings']);

?>
<?php if( $comment_count ){ ?>
<section class="comments">
	<h3><?php echo $comment_count == 1 ? 'One comment' : $comment_count . ' comments'; ?> on this post:</h3>

	<ol>
		<?php 
		//just show normal comments
		wp_list_comments( array(
			'type' 		=> 'comment',
			'avatar_size' 	=> 50,
		) ); 
		?>
	</ol>

	<div class="pagination">
		<?php previous_comments_link(); ?>
		<?php next_comments_link(); ?>
	</div>

</section>
<?php } //end if there are comments ?>

<section class="comments-form">
	<?php comment_form(); ?>
</section>

<?php if( $pings_count ){ ?>
<section class="pings">
	<h3><?php echo $pings_count == 1 ? 'One site' : $pings_count . ' sites' ; ?> mention this post:</h3>
	<ol>
		<?php 
		//just show pingbacks and trackbacks
		wp_list_comments( array(
			'type' 		=> 'pings', //pingbacks and trackbacks
			'short_ping' 	=> true,
		) ); 
		?>
	</ol>	
</section>
<?php } //end if there are pings ?>

functions.php

<?php
//Add this filter to the end of the current functions.php file:


/**
 * Fix the Number of comments to only include REAL comments (not pingbacks or trackbacks)
 */
add_filter( 'get_comments_number', 'portfolio_comment_count' );
function portfolio_comment_count(){
	//get the current post id
	global $id;
	$comments = get_approved_comments( $id );
	$comment_count = 0;
	foreach ( $comments as $comment ) {
		//only count it if it is a "normal" comment
		if( $comment->comment_type == "" ){
			$comment_count++;
		}
	}
	return $comment_count;
}