Go to CPanel->PHPMyAdmin then find the database name from the drop down menu and select it. You will see the current database tables and data on the left. From the tabs on the right Click on EXPORT, then select as FILE. You can do also ZIP Archive -- for larger databases.

This process may take from few seconds up to minutes depending on the size of your database and number of rows.

You should be prompted to save a file containing this archive when the export data process is finished. If you get timeout error please try again, if that does not work contact the Server Administrators for manual backup.