Do I need to use drupal_mail after the hook_form_contact_site_form_alter? I have added on field in my site wide contact form through this code :

    function cstm_form_contact_site_form_alter(&amp;$form, &amp;$form_state, $form_id) {

    // Add a phone number field to the contact form.
    $form['phone'] = array(
    '#type' =&gt; 'textfield',
    '#maxlength' =&gt; 20,
    '#title' =&gt; t('Your phone'),
    );

    // Define the order of the top level elements on the form (include those from contact_site_form().
    $order = array('name', 'mail', 'phone', 'subject', 'cid', 'message', 'copy', 'actions');

    // Order the elements by changing their #weight property.
    foreach($order as $key =&gt; $field) {
    $form[$field]['#weight'] = $key;
    }
    }


Now Do I need to add drupal_mail with phone number into it or Drupal will consider it automatically ? As I am new to drupal I don't know much about it.
You should use hook_mail_alter().

hook_mail_alter() allows you to modify the email cleanly before it is sent. The Contact module passes the entire form state to drupal_mail(), so you have access to it in this alter hook via the params key.

A quick example. I haven't tested it:

function my_module_mail_alter(&amp;$message) {
  if ($message['id'] == 'contact_page_mail') {
    $phone = $message['params']['phone'];

    $message['body'][] = "Phone number: " . check_plain($phone);
  }
}


Let me know if that works.