demo.module

<?php

/**
 * @file
 * Demo module, Basic Ajax form submit (Ajax framework).
 */

 /**
  * Implements hook_menu().
  */
function demo_menu() {
  return array(
    'demo/newsletter' => array(
      'page callback' => 'drupal_get_form',
      'page arguments' => array('demo_demo_form'),
      'access callback' => TRUE,
      'type' => MENU_CALLBACK,
    ),
  );
}

 /**
  * A simple newsletter subscribe form.
  */
function demo_demo_form($form, &$form_state) {
  return array(
    'email' => array(
      '#type' => 'textfield',
      '#title' => t('Join our Newsletter'),
      '#required' => TRUE,
      '#attributes' => array(
        'placeholder' => t('mail@example.com'),
      ),
    ),
    'submit' => array(
      '#type' => 'submit',
      '#value' => t('Subscribe'),
      '#ajax' => array(
        'callback' => 'demo_form_ajax_submit',
        'wrapper' => 'demo-demo-form',
        'method' => 'replace',
        'effect' => 'fade',
      ),
    ),
  );
}

/**
 * Ajax callback function.
 */
function demo_form_ajax_submit($form, $form_state) {
  // Dummy/dumb validation for demo purpose.
  if (!empty($form_state['input']['email'])) {
    return 'Subscribed !';
  }
  else {
    return $form;
  }
}