Views allows handlers to output form elements, wrapping them automatically in a form, and handling validation / submission. The form is multistep by default, allowing other modules to add additional steps, such as confirmation screens.

Implementation

A views handler outputs a special placeholder in render(), while the real form with matching structure gets added in views_form(). When the View is being preprocessed for the theme file, all placeholders get replaced with the rendered form elements. The views handler can also implement views_form_validate() and views_form_submit().
  function render($values) {
    return '<!--form-item-' . $this->options['id'] . '--' . $this->view->row_index . '-->';
  }

  function form_element_name() {
    // Make sure this value is unique for all the view fields
    return $this->options['id'];
  }

  function form_element_row_id($row_id) {
    // You could use values from $this->view->result[$row_id]
    // to provide complex row ids.
    return $row_id;
  }

  function views_form(&$form, &$form_state) {
    // The view is empty, abort.
    if (empty($this->view->result)) {
      return;
    }

    $field_name = $this->form_element_name();
    $form[$field_name] = array(
      '#tree' => TRUE,
    );
    // At this point, the query has already been run, so we can access the results
    foreach ($this->view->result as $row_id => $row) {
      $form_element_row_id = $this->form_element_row_id($row_id);
      $form[$field_name][$form_element_row_id] = array(
        '#type' => 'textfield',
        '#title' => t('Your name'),
        '#default_value' => '',
      );
    }
  }

  // Optional validate function.
  function views_form_validate($form, &$form_state) {
    $field_name = $this->form_element_name();
    foreach ($form_state['values'][$field_name] as $row_id => $value) {
      if ($value == 'Drupal') {
        form_set_error($field_name . '][' . $row_id, "You can't be named Drupal. That's my name.");
      }
    }
  }

  // Optional submit function.
  function views_form_submit($form, &$form_state) {
    // Do something here
  }
The form is multistep by default, with one step: 'views_form_views_form'. A "form_example" module could add a confirmation step by setting:
 $form_state['step'] = 'form_example_confirmation';
in form_example_views_form_submit(). Then, views_form would call form_example_confirmation($form, $form_state, $view, $output) to get that step. Important: You can fetch the Views object in form_alter and validate / submit hooks from the form state:
  $view = $form_state['build_info']['args'][0];

Relevant Views functions

Hooks