client.js

jQuery.post(
    my_foobar_client.ajaxurl, 
    {
        'action': 'foobar',
        'foobar_id':   123
    }, 
    function(response) {
        console.log('The server responded: ', response);
    }
);

wp-minimal-plugin.php

<?php 
/*
Plugin Name: Formscript
Description: includes form xyz.
Author: Yannik Preiß
*/

add_action( 'wp_ajax_foobar', 'my_ajax_foobar_handler' );

function my_ajax_foobar_handler() {
    // Make your response and echo it.

    // Don't forget to stop execution afterward.
    wp_die();
}