For those not acquainted with Silex: Silex is a PHP microframework for PHP 5.3 A microframework provides the guts for building simple single-file apps. It's awesome. For the example, I've setup a virtual host of example.local on my development machine.
He includes the contents of the .htaccess you'll need to get the rewrite to work for Silex, a link to the OAuth extension you'll need to install for PHP and the code to make the login and auth routes. You'll need to create a Twitter application for your site to get the OAuth secret key to make the authentication work. You can see the complete code here.