You will need a script that integrates with the phpBB framework. Something like this should work.

<?php
define('IN_PHPBB', true);
$phpbb_root_path = (defined('PHPBB_ROOT_PATH')) ? PHPBB_ROOT_PATH : './';
$phpEx = substr(strrchr(__FILE__, '.'), 1);
include($phpbb_root_path . 'common.' . $phpEx);

// Start session management
$user->session_begin();
$auth->acl($user->data);
$user->setup();
?>

Then, look at the $auth->login() function (an example use is in the login_box() function in /includes/functions.php). A simplistic yet incomplete example is:

$result = $auth->login($username, $password); // There are more params but they're optional

if ($result['status'] == LOGIN_SUCCESS)
{
    // Logged in
}
else
{
    // Something went wrong
}