How do I customize the date-submit part in comment section?
You can use format_interval() to do this.

function MYTHEME_preprocess_comment(&amp;$variables) {
  $comment = $variables['elements']['#comment'];
  $variables['created'] = t('@created ago', array(
    '@created' =&gt; format_interval(REQUEST_TIME - $comment-&gt;created),
  ));
}


If you look at the source for template_preprocess_comment(), you are essentially just using format_interval() instead of format_date() to create the timestamps.  In the above, we run everything through t() so that the string "ago" gets translated properly.