Best way for Ajax+jQuery form validation & submission? Included a demo link inside

I have created a small modal box in jQuery which loads a message form. If you enter some text and hit submit the button replaces with a loading .gif and closes the modal box. However I don't know how to properly 开发者_开发技巧send the form data to a backend script, maybe in PHP.

There is a whole subset of Ajax for jQuery but I've been struggling to get this working. Any help would be more than appreciated. Demo link: Link got taken down sorry!