Theming forms in your theme

An example about how to theme Drupal Commerce Check Out form:

template.php

/**
 * Implements hook_theme().
 */
function yourtheme_theme($existing, $type, $theme, $path) {
  $base = array(
    'render element' => 'form',
    'path' => drupal_get_path('theme', 'yourtheme') . '/templates/forms',
  );

  return array(
    'commerce_checkout_form_checkout' => $base + array(
      'template' => 'commerce-checkout-form-checkout',
    ),
  );
}

/**
 * Preprocessor for commerce_checkout_form_checkout theme.
 */
function yourtheme_preprocess_commerce_checkout_form_checkout(&$variables) {
  /* Add or modify your variables */
}

[yourtheme]/templates/forms/commerce-checkout-form-checkout.tpl.php

<?php
  // Render or hide parts of $form: var_export($form);
  // Example given:
  hide($form['title']);
  print render($form['first']);
  // Render remaining form elements as usual.
  print drupal_render_children($form);
?>

Don't forget clearing the theme registry cache.