The best method for moving MySQL databases is to export them from your PHPMyAdmin tool. If you do not have PHPMyAdmin already installed, you can do so through Site Manager >> Install & Manage. The PHPMyAdmin tool is accessible via your Site Manager username and password through http://yourdomain.com/pma/.
Click on the database name that you would like to migrate and utilize the default options in the "Export" tab.
Once exported and thus backed up on your local machine, you can set up the databases and associated username/password combinations through cPanel >> MySQL Database Wizard. You will need to use the wizard for EACH database that you need to set up. Do not lose the database username and password that you set up for each database. Be sure to save them in a notepad or write them down as you are moving them.
Once complete, you can connect to cPanel >> PHPMyAdmin (Note: PHPMyAdmin is installed by default on all cPanel servers) to navigate to each database. Use the "Import" tab to upload the backup files for each database.
If you run into any downloading or uploading trouble with your databases, please contact our expert technical support staff. They are happy to assist you and answer any questions you may have.