You'll most likely need to ask the service provider to create your database; create your account, and named database, and give you the server address.
Once that's done, there are various tools available. I've been using "phpMyAdmin" (http://www.phpwizard.net/projects/phpMyAdmin/), which is a PHP based DB client.
Beyond that, you can write your own MySQL manipulation code in your choice of server-side languages (PHP, Perl, etc).