How can I add an operation to the node and user lists?
If you look at the User module in DRUPAL_ROOT/modules/user you'll see the user_menu() function:
http://api.drupal.org/api/drupal/modules!user!user.module/function/user_menu/7

You can add your own operation by making your own hook_menu() that mimics what Core does for the "Permissions" Operation. Its also important to note that these tabs or drop down operations (depending on your theme) are essentially defined as MENU_LOCAL_TASK items in the drupal menu system. See below:

// What Core does in user_menu() ...
 // Permissions and role forms.
  $items['admin/people/permissions'] = array(
    'title' =&gt; 'Permissions', 
    'description' =&gt; 'Determine access to features by selecting permissions for roles.', 
    'page callback' =&gt; 'drupal_get_form', 
    'page arguments' =&gt; array('user_admin_permissions'), 
    'access arguments' =&gt; array('administer permissions'), 
    'file' =&gt; 'user.admin.inc', 
    'type' =&gt; MENU_LOCAL_TASK,
  );



// You do something similar in your own module ...
  function mymodule_menu() {
    $items['admin/people/foobar_operation'] = array(
      'title' =&gt; 'Foo Bar Operation', 
      'description' =&gt; 'A form with my custom settings', 
      'page callback' =&gt; 'drupal_get_form', 
      'page arguments' =&gt; array('yourmodule_foobar_permission'), 
      'access arguments' =&gt; array('administer yourmodule permissions'), 
      'file' =&gt; 'yourmodule.admin.inc',
      'type' =&gt; MENU_LOCAL_TASK,
    );

    // Do the same for stuff under admin/content.

    return $items;
  }


Hopefully this tidbit helps...