AJAX Requests with Native WordPress Features. See http://cfxdesign.com/ajax-requests-with-native-wordpress-features

wp_ajax-localize_script.php

<?php

function localize_ajax_variables() {
  wp_localize_script('your_js', 'wp_ajax_vars', array(
    'admin_url' => admin_url('admin-ajax.php')
  ));
}
add_action('wp_enqueue_scripts', 'localize_ajax_variables', 999);

wp_ajax.js

var theForm = '#heart > form';

function likeUpdated(data) {
  $(theForm).find('.fa-refresh').removeClass('fa-spin fa-refresh').addClass('fa-heart');
  $('.likes').text(data.likes);
  $(theForm).find('button').removeAttr('disabled');
}

$(function() {
  var options = {
    url:      (typeof wp_ajax_vars !== 'undefined') ? wp_ajax_vars.admin_url : '',
    dataType: 'json',
    data:     {
                action: 'update_likes_ajax'
              },
    success:  likeUpdated
  };
  $(document).on('submit', theForm, function(e) {
//    $(this).find('button').attr('disabled', 'disabled');
//    $(this).find('.fa-heart').removeClass('.fa-heart').addClass('fa-refresh fa-spin');
    $(this).ajaxSubmit(options);
    e.preventDefault();
  });

});

wp_ajax_function-complete.php

<?php

function update_likes() {
  if(!empty($_POST['like_nonce'])) {
    if(defined('DOING_AJAX') && DOING_AJAX) {
      check_ajax_referer('like-nonce', 'like_nonce', true);
    } elseif(!wp_verify_nonce($_POST['like_nonce'], 'like-nonce')) {
      wp_redirect($_POST['redirect']);
      exit;
    }

    $likes = get_post_meta($_POST['post'], '_post_likes', true);
    if(!is_numeric($likes)) {
      $likes = 0;
    }
    $likes += 1;
    update_post_meta($_POST['post'], '_post_likes', $likes);

    if(defined('DOING_AJAX') && DOING_AJAX) {
      echo json_encode(array('likes' => $likes));
      die();
    }
    wp_redirect($_POST['redirect']);
    exit;
  }
}
add_action('init', 'update_likes');
add_action('wp_ajax_update_likes_ajax', 'update_likes');
add_action('wp_ajax_nopriv_update_likes_ajax', 'update_likes');

wp_ajax_function-no_ajax.php

<?php

function update_likes() {
  if(!empty($_POST['like_nonce'])) {
    if(!wp_verify_nonce($_POST['like_nonce'], 'like-nonce')) {
      wp_redirect($_POST['redirect']);
      exit;
    }

    $likes = get_post_meta($_POST['post'], '_post_likes', true);
    if(!is_numeric($likes)) {
      $likes = 0;
    }
    $likes += 1;
    update_post_meta($_POST['post'], '_post_likes', $likes);

    wp_redirect($_POST['redirect']);
    exit;
  }
}
add_action('init', 'update_likes');

wp_ajax_markup.html

<div class="post-like" id="heart">
  <form method="post">
    <?php $likes = get_post_meta(get_the_ID(), '_post_likes', true); ?>
    <input type="hidden" name="like_nonce" value="<?php echo wp_create_nonce('like-nonce'); ?>">
    <input type="hidden" name="post" value="<?php the_ID(); ?>">
    <input type="hidden" name="redirect" value="<?php echo get_the_permalink().'#heart'; ?>">
    <span class="likes"><?php echo empty($likes) ? '' : $likes; ?></span>
    <button type="submit">
      <span class="fa-stack fa-lg">
        <i class="fa fa-circle fa-stack-2x"></i>
        <i class="fa fa-heart fa-stack-1x fa-inverse"></i>
      </span>
    </button>
  </form>
</div>