I copied
/themes/bartik/templates/comment.tpl.php
to/sites/all/themes
And modified
/sites/all/themes/comment.tpl.php
This will definitely not work. The content of the new file will not be rendered at all, and Drupal will not even care about this file, because you are not using the theme format that Drupal expects.
Modifying the original theme is NOT a good practice, that's correct. If you would like to make slight modifications to the original theme, you have to create a subtheme, which inherits the parent theme's resources.
- There's a good tutorial on drupal.org about the theory of creating subthemes (where the base theme is Bartik):
Creating a sub-theme (https://drupal.org/node/225125) - You can read about the theme's .info file here: https://drupal.org/node/171205
- And here's a really short summary about creating a D7 subtheme: http://www.slideshare.net/AdolfoNasol/creating-drupal-7-subtheme
After enabling the new subtheme, you can copy Bartik's comment.tpl.php
to the new subtheme's templates
directory, clear cache, and enjoy modifying your own theme's files based on Bartik without worrying about the original ones.
Btw. I suggest you using Drupal Answers: https://drupal.stackexchange.com/.