To make a Drupal module that provides triggers you need to

1. Use module_invoke_all at the point your code triggers an event.
   <?php
module_invoke_all('mymodule', $op, $arg1, $arg2, ....);
?>

   This basically defines a hook that your module provides - it has to be called after the name of your module because of a bug

2. Define your modules implementation of this hook to run any actions registered for it.
   <?php


function mymodule_mymodule($op, $arg1, $arg2...){
   $aids = _trigger_get_hook_aids('mymodule', $op);
   $context = array(
     'hook' => 'mymodule',
     'op' => $op,
     'arg2' => $arg2,
      (arg3 etc)
   );
   actions_do(array_keys($aids), $arg1, $context);

}
?>

   You can wrap up as many arguments as you like in the context array, $op can be used to define related actions like the way the user module has op for insert, delete, update etc.

   $arg1 is passed by reference as the $object parameter to actions.

3. Tell Drupal about your triggers by implementing hook_hook_info

   This adds the triggers on the triggers admin page

   <?php
function mymodule_hook_info() {
  return array(
      'mymodule' => array(
        'mymodule' => array(
          'some_op' => array(
            'runs when' => t('Text to explain when the trigger runs'),
           ),
           'some_other_op' => array(
             'runs when' => t('more user text'),
           ),
         ),
       ),
   );
}
?>

4. Now you can use the admin interface to run actions when your triggers fire.

See Writing triggers (Drupal 6.x) for more details - I wrote this up as I found it helpful to approach the issue in reverse order to that page.