Submit form using AJAX and jQuery

First give your form an id attribute, then use code like this:

$(document).ready( function() {
  var form = $('#my_awesome_form');

  form.find('select:first').change( function() {
    $.ajax( {
      type: "POST",
      url: form.attr( 'action' ),
      data: form.serialize(),
      success: function( response ) {
        console.log( response );
      }
    } );
  } );

} );

So this code uses .serialize() to pull out the relevant data from the form. It also assumes the select you care about is the first one in the form.

For future reference, the jQuery docs are very, very good.