multiple_submit_buttons.module

<?php

// Implements hook_menu()
function multiple_submit_buttons_menu() {
  $items['demo/multiple_submit_buttons/form'] = array(
    'page callback' => 'drupal_get_form',
    'page arguments' => array('multiple_submit_buttons_customform_form'),
    'access callback' => TRUE,
    'type' => MENU_CALLBACK,
  );
  
  return $items;
}

function multiple_submit_buttons_customform_form($form, $form_state) {
  $form = array(
    'name' => array(
      '#type' => 'textfield',
      '#title' => 'Enter your name',
      '#maxlength' => '128',
    ),
    'actions' => array(
      'forward' => array(
        '#type' => 'submit',
        '#value' => 'Forwards',
      ),
      'backward' => array(
        '#type' => 'submit',
        '#value' => 'Backwards',
      ),
    ),
  );
  
  return $form;
}

function multiple_submit_buttons_customform_form_validate($form, &$form_state) {
  if ($form_state['values']['op'] == 'Forwards') {
    drupal_set_message('This validation only runs when you click the forward button.');
  } elseif ($form_state['values']['op'] == 'Backwards') {
    drupal_set_message('This validation only runs when you click the backwards button.');
  } else {
    drupal_set_message('Unknown Action chosen');
  }
  return TRUE;
}

function multiple_submit_buttons_customform_form_submit($form, &$form_state) {
  if ($form_state['values']['op'] == 'Forwards') {
    drupal_set_message('This is your string forwards: ' . $form_state['values']['name']);
  } elseif ($form_state['values']['op'] == 'Backwards') {
    drupal_set_message('You chose to print your input out backwards: ' . strrev($form_state['values']['name']));
  } else {
    drupal_set_message('We aren\'t sure what you wanted to do, but your input is:  ' . $form_state['values']['name']);
  }
}