How to hook contact form of drupal 7 for custom styling?
Or you can use hook_form_FORM_ID_alter() to get the specific contact form. hook_form_alter() will run for every form on the page.

function MYMODULE_form_contact_site_form_alter(&amp;$form, &amp;$form_state, $form_id) {
  $form['name']['#attributes']['class'] = array('class1', 'class2');

  $form['mail']['#attributes']['class'] = array('class1', 'class2');

  $form['subject']['#attributes']['class'] = array('class1', 'class2');

  $form['message']['#attributes']['class'] = array('class1', 'class2');

  // add class to the overall form
  $form['#attributes']['class'] = array('class1');
}


If you don't know how to use custom modules, you'd have to research that first. Dropping this function in and replacing MYMODULE with your module name will make this work.