How to add a stylesheet in Drupal for a module

Attaching a CSS file via your module is so simple it's not really documented, that Agaric could find with these searches:

drupal add style sheets to module
drupal add stylesheet modules
attach CSS

How to add CSS in Drupal 5

This example is from the book module:

    drupal_add_css(drupal_get_path('module', 'book') .'/book.css');

So for your module "example_module," with "example_module_extra_style.css" in a folder css within your module directory, the code would look like this:

drupal_add_css(drupal_get_path('module', 'example_module') .'/css/example_module_extra_style.css');

The book module puts this call in the non-cache portion of the menu hook (if(!$may_cache)); it should be called where it's needed. If it's only going to be rarely used, tell Drupal not to aggregate it with all the other stylesheets. New code is emphasized, the first two new attributes ($type and $media, respectively) are set to their defaults, but have to be there in order to set the preprocess flag:

drupal_add_css(drupal_get_path('module', 'example_module') . '/css/rare_extra_style.css', <em>'module', 'all', FALSE</em>);

The Drupal API documents the drupal_add_css function.