Adding the following code to the top of the PHP file will give you access to the WordPress functions and global variables.
<?php include_once($_SERVER['DOCUMENT_ROOT'].'/wp-load.php' );
You should then be able to run normal WordPress functions to determine whether or not the user is logged in:
<?php
global $user_ID;
get_currentuserinfo();
if ($user_ID) {
// Do Something
}
?>