Hey Robbie,
I just completed that type of install.
Change the lines in config.php
$CFG->dbhost = 'yourwebsite.org'; // no leading "http:// or www.
$CFG->dbname = 'your database name on the remote server'; // database name, eg moodle
Then, contact support at the site you're sending too and have them set up to allow access to the MySql from the sending server. Be aware that it does present some security issues.