Form ajax.html

<form>
  <!-- Hidden Required Fields -->
  <input type="hidden" name="project_name" value="Site Name">
  <!-- <input type="hidden" name="admin_email" value="admin@mail.com"> -->
  <input type="hidden" name="form_subject" value="Form Subject">
  <!-- END Hidden Required Fields -->

  <input type="text" name="name" placeholder="You name..." required><br>
  <input type="text" name="email" placeholder="You E-mail..." required><br>
  <input type="text" name="phone" placeholder="You phone..."><br>
  <button>Send</button>
</form>

jQuery Form Ajax.js

//Ajax отправка форм
//Документация: http://api.jquery.com/jquery.ajax/
$('#form1, #form2').on('submit', function(e) {
  var $this = $(this);
  e.preventDefault();
  $.ajax({
    type: 'POST',
    url: 'mail.php',
    data: $this.serialize()
  }).done(function() {
    alert('Спасибо за заявку!');
    //setTimeout(function() {
      //$this.trigger('reset');
      //$.fancybox.close();
    //}, 1000);
    success();
  });
});

function success() {

  setTimeout(function() {
    $('.loader').fadeIn(200);
    setTimeout(function() {
      $('.reply').fadeIn(300);
      setTimeout(function() {
        $('.loader').fadeOut(200);
        $('#form1').trigger('reset');
        $('.reply').fadeOut(300);
        $('.modal').fadeOut(300);
        $('.overlay').fadeOut(300);
      }, 3000);
    }, 2000);
  }, 500);

}

How to use uniMail
Include jQuery;
Include Ajax code from script.js;
Change Ajax selector in you JS;
Create HTML form with you form class;
Create HTML Hidden Required Fields with you values;
Change path to mail.php in you JS.
Done!

mail.php

<?php
$method = $_SERVER['REQUEST_METHOD'];
//Script Foreach
$c = true;
if ( $method === 'POST' ) {
  $project_name = trim($_POST["project_name"]);
  // $admin_email  = trim($_POST["admin_email"]);
  $admin_email  = 'info@my-site.com'; //Here write hosting email
  $copy_email = 'copy1@gmail.com, copy2@gmail.com'; //copy
  $form_subject = trim($_POST["form_subject"]);
  foreach ( $_POST as $key => $value ) {
    if ( $value != "" && $key != "project_name" && $key != "admin_email" && $key != "form_subject" ) {
      $message .= "
      " . ( ($c = !$c) ? '<tr>':'<tr style="background-color: #f8f8f8;">' ) . "
        <td style='padding: 10px; border: #e9e9e9 1px solid;'><b>$key</b></td>
        <td style='padding: 10px; border: #e9e9e9 1px solid;'>$value</td>
      </tr>
      ";
    }
  }
} else if ( $method === 'GET' ) {
  $project_name = trim($_GET["project_name"]);
  // $admin_email  = trim($_GET["admin_email"]);
  $admin_email  = 'info@my-site.com'; //Here write hosting email
  $copy_email = 'copy1@gmail.com, copy2@gmail.com'; //copy
  $form_subject = trim($_GET["form_subject"]);
  foreach ( $_GET as $key => $value ) {
    if ( $value != "" && $key != "project_name" && $key != "admin_email" && $key != "form_subject" ) {
      $message .= "
      " . ( ($c = !$c) ? '<tr>':'<tr style="background-color: #f8f8f8;">' ) . "
        <td style='padding: 10px; border: #e9e9e9 1px solid;'><b>$key</b></td>
        <td style='padding: 10px; border: #e9e9e9 1px solid;'>$value</td>
      </tr>
      ";
    }
  }
}
$message = "<table style='width: 100%;'>$message</table>";
function adopt($text) {
  return '=?UTF-8?B?'.Base64_encode($text).'?=';
}
$headers = "MIME-Version: 1.0" . PHP_EOL .
"Content-Type: text/html; charset=utf-8" . PHP_EOL .
'From: '.adopt($project_name).' <'.$admin_email.'>' . PHP_EOL .
'Cc:'.$copy_email.PHP_EOL .
'Reply-To: '.$admin_email.'' . PHP_EOL;
$sended = mail($admin_email, adopt($form_subject), $message, $headers );
echo json_encode($sended);

?>