Well based on the fact that you are talking about PHP, I assume that means you do know your host has PHP? Create a .php file that contains:
<?php phpinfo(); ?>
Then go to that .php file using your browser. Look in the "Configure Command" section, if it has --with-mysql, then the PHP installed on your system allows access to MySQL, if it doesn't have it then MySQL support is not enabled. That won't actually tell you if YOU have access to MySQL (a login/password) it will just tell you if MySQL support is enabled.