[PHP] Connecting to MySQL DB on remote controlled PC


//name of PC is rottserver
mysql_connect("localhost", "rottserver", "password_here") or die(mysql_error());

How would I go about connecting to my database online?

If I have to host the database, anyone have some free MySQL hosting options?
(P.S. if this helps, I’m willing to dedicate this computer to hosting the database if at all possible)