Basic Drupal multipart form example with Previous and Next buttons

gistfile1.php

<?php

/**
 * Implementation of hook_menu().
 */
function test_menu() {
  $items = array();
  // Form page.
  $items['test/form'] = array(
    'title' => t('Test Form'),
    'page callback' => 'test_page',
    'page arguments' => array(),
    'access arguments' => array('access content'),
  );
  // Success page.
  $items['test/success'] = array(
    'title' => t('Test successful!'),
    'page callback' => 'test_success',
    'page arguments' => array(),
    'access arguments' => array('access content'),
  );
  return $items;
}

/**
 * Page used to display the form (all steps).
 */
function test_page() {
  return drupal_get_form('test_form');
}

/**
 * Simple confirmation page displayed after finishing the form.
 */
function test_success() {
  return 'OK!';
}

/**
 * Form generation.
 */
function test_form($form_state) {

  // Get the current step, either from previously posted value, or just set it to 1.
  $step = (isset($form_state['storage']['step'])) ? $form_state['storage']['step'] : 1;

  switch ($step) {

    case 1:

      // Custom page title.
      drupal_set_title('Step 1');

      // Current step declaration.
      $form['step'] = array(
        '#type' => 'hidden',
        '#value' => 1,
      );

      // All the real form fields.
      $form['step1_field1'] = array(
        '#title' => 'Step 1 Field 1',
        '#type' => 'textfield',
        '#default_value' => $form_state['storage']['values'][1]['step1_field1'],
      );

      // Submit button(s).
      // Only 'Next' here, as we are on the first step.
      $form['next'] = array(
        '#type' => 'submit',
        '#value' => 'Next',
      );

      // Not important - used only for displaying values posted so far.
      $form['posted_values'] = array(
        '#type' => 'markup',
        '#value' => _test_display_posted_values($form_state),
      );
      break;

    case 2:

      // Custom page title.
      drupal_set_title('Step 2');

      // Current step declaration.
      $form['step'] = array(
        '#type' => 'hidden',
        '#value' => 2,
      );

      // All the real form fields.
      $form['step2_field1'] = array(
        '#title' => 'Step 2 Field 1',
        '#type' => 'textfield',
        '#default_value' => $form_state['storage']['values'][2]['step2_field1'],
      );

      // Submit button(s).
      // Both 'Prev' and 'Next' on all middle steps.
      $form['prev'] = array(
        '#type' => 'submit',
        '#value' => 'Prev',
      );
      $form['next'] = array(
        '#type' => 'submit',
        '#value' => 'Next',
      );

      // Not important - used only for displaying values posted so far.
      $form['posted_values'] = array(
        '#type' => 'markup',
        '#value' => _test_display_posted_values($form_state),
      );
      break;

    case 3:

      // Custom page title.
      drupal_set_title('Step 3');

      // Current step declaration.
      $form['step'] = array(
        '#type' => 'hidden',
        '#value' => 3,
      );

      // All the real form fields.
      $form['step3_field1'] = array(
        '#title' => 'Step 3 Field 1',
        '#type' => 'textfield',
        '#default_value' => $form_state['storage']['values'][3]['step3_field1'],
      );

      // Submit button(s).
      // 'Prev' and 'Submit' here, as we are on the last step.
      $form['prev'] = array(
        '#type' => 'submit',
        '#value' => 'Prev',
      );
      $form['submit'] = array(
        '#type' => 'submit',
        '#value' => 'Finish',
      );

      // Not important - used only for displaying values posted so far.
      $form['posted_values'] = array(
        '#type' => 'markup',
        '#value' => _test_display_posted_values($form_state),
      );
      break;
  }
  return $form;
}

function test_form_submit($form, &$form_state) {

  // Save all posted values for $form_state['storage']
  // to make them available in all other steps.
  $form_state['storage']['values'][$form_state['values']['step']] = $form_state['values'];

  // Deal with current step number based on which submit button was clicked.
  switch ($form_state['values']['op']) {

    case 'Next':
      // Do not finally submit the form yet, rebuild it instead.
      $form_state['rebuild'] = TRUE;
      // Go to next step.
      $form_state['storage']['step'] = ++$form_state['values']['step'];
      break;

    case 'Prev':
      // Do not finally submit the form yet, rebuild it instead.
      $form_state['rebuild'] = TRUE;
      // Go to previous step.
      $form_state['storage']['step'] = --$form_state['values']['step'];
      break;

    case 'Finish':
      // Do something with all form values ($form_state['storage']) before unsetting it.
      // ...
      // And then unset it.
      unset($form_state['storage']);
      // This was the final step, so redirect to success page.
      $form_state['redirect'] = 'test/success';
      break;
  }
}

function _test_display_posted_values($form_state) {
  $output = '<p>Posted values:</p>'
          . '<p>Step 1 field 1: ' . $form_state['storage']['values'][1]['step1_field1'] . '</p>'
          . '<p>Step 2 field 1: ' . $form_state['storage']['values'][2]['step2_field1'] . '</p>'
          . '<p>Step 3 field 1: ' . $form_state['storage']['values'][3]['step3_field1'] . '</p>';
  return $output;
}