Usually, I just create one php page and leave it as index.php and use variables to call all other pages.
This works fine, but I'd rather not develop sites this way. I can easily add my page code to each page in the directory, but I want to use one central document for governing all my PHP. What is the most professional way to handle this? I can think of many solutions, but what is the paradigm?
That's the going paradigm. The major frameworks do it this way. For example, Zend, Symfony, CakePHP, CodeIgniter, and others -- they each have you define a mapping between an external URL and an internal action to perform.