To create a mysql database, log into your control panel and select the 'MySQL Databases' link.
Enter in the name of the database you want to create and submit it.
Once you have created a database you must create a database user and then grant that user access to the database you created. This is all done through the same mysql manager page.
Once you have a mysql database and username you can manage it via your shell account, or via phpMyAdmin which is located in your control panel.
Make sure you are using the correct login/password and database name as listed on the mysql manager as they will not be exactly the same as the name you entered in when you created the database.