JSFiddle - React, Tailwind, and code Playground

HTML

<input type='text' id='short'>
<input type='button' id='shorten_btn' value='shorten'>

JavaScript

var $short = $("#short"),
	$btn = $("#shorten_btn"),
    url;

$btn.on('click', function (e) {
    url = $short.val();
    shorten();
});

function shorten() {
    alert("SHORTENING");
    $.ajax({
        url: '/your_script.php', // Pointed at your php script
        type: 'POST', // Or GET - totally optional
        data: 'url=' + url, // Your args
        dataType: 'text', // Define the type of data you will get back
        success: function (data) {
            // Data should be your echoed data
            // This is faking it
            $short.val(data);
        }
    });
}