Customize the Search Block in Drupal 7 (from https://www.drupal.org/node/1021902)

Add Font Awesome on a Drupal form submit button.php

function MYTHEME_form_alter(&$form, &$form_state, $form_id) {
  if ($form_id == 'search_block_form') {
    $form['actions']['button']['#prefix'] = '<button type="submit">';
    $form['actions']['button']['#suffix'] = '</button>';
    $form['actions']['button']['#markup'] = '<i class="icon-search"></i>';
  }
} 

Programmatically embed the Search Block in Drupal 7.php

function template_preprocess_page(&$variables){
  $search_form = drupal_get_form('search_form');
  $search_form_box = drupal_render($search_form);
  $variables['search_box'] = $search_form_box;
}