You can access your MySQL databases using PHPMyAdmin. This application can be found on https://phpmyadmin.ulyssis.org. To login you need to use your MySQL password, this password is different from your account password for security reasons as well as convenience. In case you've forgotten your MySQL password you can get it from your websites configuration file. This is usually called config.php, wp-config.php, settings.php or something similar.
On the left you will see your username, you can click the plus sign to reveal all your databases. You can then view databases and tables. For each table you can view the records, view and change the structure, add records, take backups, etc.
To take a backup of all your databases you simple select "Export" on the main menu and press start. You can later restore backups by uploading the file to the "Import" page.