Override comment.tpl.php file with theme
You should be able to override Drupal's default comment.tpl.php file by copying it from /modules/comment into your theme directory. From there, edit the file as needed. Then clear the cache (on the Admin > Site configuration > Performance), so that the theme cache will get rebuilt and your new theme file will get recognized.

You would only need to rename comment.tpl.php to comment-[type].tpl.php, if you wanted to override comment theming differently for different node types.