How do I properly add css to my feature? I have a feature that just contains a few views. How do I properly add a stylesheet to it?
You add the css file to the module.
Use drupal_add_css to include the css file in the .module, this could be done in hook_init and would look something like this:

module_name_init() {
  if (arg(0) == 'views_path') {
    drupal_add_css(drupal_get_path('module', 'module_name') . '/path_to.css');
  }
}