First time doing Ajax with WP, how to do it?

$('#shoes-kids').on('change', function(){
$.post('<?php echo admin_url( "admin-ajax.php" ); ?>',  {
          first_name: ""+ $("#first_name").val(), //sending first name
          last_name: ""+ $("#last_name").val(), //sending last name
      action : 'your_ajax_hook'
        },  function(data,status){
            if(status=="success")
        {
         $("#product-results").append(data);
        }
        else
        {
        alert('Failed');
        }
    });
 });

i.e:-

add_action( 'wp_ajax_your_ajax_hook', 'your_function_name' );
add_action( 'wp_ajax_nopriv_your_ajax_hook', 'your_function_name'  );

In above I have send first_name and last_name as a post data you can sent more by just putting ‘,’ as a separator