var html = `
  <form>
    <input type="text" name="firstname" placeholder="Имя"/>
    <input type="text" name="lastname" placeholder="Фамилия"/>
    <button type="submit">Отправить</button>
  </form>
`;

$('body').append(html);

// 1
$('form').on('submit', function(event) {
  event.preventDefault();
  console.log({
    firstname: $('input[name="firstname"]', this).val(),
    lastname: $('input[name="lastname"]', this).val(),
  });
});

// 2
// $('form').on('submit', function(event) {
//  event.preventDefault();
//  console.log($(this).serializeArray());
// });