You can export and import the contents of any database on your account using phpMyAdmin.
You will first need to login to the database using phpMyAdmin - please follow this article if you are unsure how to do this.
Exporting your database
Select the database that you wish to copy from the left hand column
Now click Export from the tabs along the top.
On the export page, leave everything as default and tick Save as file and then Go. A copy of the database will be saved on your machine.
Importing your database
You now need to create a blank database to import this data into. If you are doing this on a Gradwell hosting service, then go to the subscription that you wish to add the database to and create a blank database. Log into it using phpMyAdmin.
Select a database from the left hand side to import the data into and then select Import from the tabs along the top.
Select the file that you downloaded to your machine. Click Go and the database should be imported. If you encounter any errors it is worthwhile entering the error text into a search engine in the first instance to see if there is a simple fix to the problem encountered.