A basic ajax request via jQuery is described as follows.

Ajax request

var data = '{
               "ESignType": {
                               "Type": "DOCUSIGN",
                               "SignCallBackURL": "www.test.com"
                            },
               "HostFormOnQuik": true,
               "QuikFormID": "1"
            }';
var token = 'PUT_TOKEN_HERE';

$.ajax({
      type: "POST",
      contentType: "application/json",
      url: "https://websvcs.quikforms.com/rest/quikformsengine/QFE/Execute",
      data: data,
      beforeSend: function (xhr) {
            xhr.setRequestHeader("Authorization", "BEARER " + token);
        }
})