Add classes to form actions in Drupal 7

hook-form-alter-add-action-classes.php

<?php

/**
 * Implements hook_form_alter().
 */
function MYTHEME_form_alter(&$form) {
  // Add additional classes to each form action.
  if (isset($form['actions'])) {
    $actions = element_children($form['actions']);
    foreach ($actions as $action) {
      $item = &$form['actions'][$action];
      // Add a generic "button" class.
      $item['#attributes']['class'][] = 'button';
      // Add a type-specific "button-{type}" class (e.g. "button-submit").
      $item['#attributes']['class'][] = 'button-' . $action;
    }
  }
}