Voy de salida, así que si nadie te ha contestado al rato trato de hacer un ejemplo, pero básicamente tienes que hacer una llamada xmlhttp por get y obtener el HTML resultante:
Cita: Receiving the shortened URL
After submitting the URL you would like shortened as specified above, an HTTP response (web page) will be returned. The response header will be "HTTP/1.1 200 OK" if the URL was shortened as expected, or "HTTP/1.1 500 Internal Server Error" if there was any problem that prevented this.
Assuming the request was successful, the body of the response will contain only the new shortened URL, in plain text.
"Si la llamada es exitosa, el body solamente contendrá la nueva URL acortada."
Saludos