Use serialize
to get a string representation of your form and then simply post it using jQuery's post
AJAX function.
Very simple example (from jQuery's website using PHP, but any URL would do):
$.post("test.php", $("#testform").serialize());
If you have multiple forms on the page you can use this code on button click to get the correct form Id (where 'someButton' can be any valid jQuery selector):
$('someButton').click(function() {
//old, less efficient code
//var formId = $(this).closest("form").attr("id");
//$.post("test.php", $("#" + formId).serialize());
//as per Vincent Robert's suggestion, simplified version
$.post("test.php", $(this).closest("form").serialize());
});