Using PHPMyAdmin, you will need to export your database, there are a number of online resources that have tutorials on how to export your database, here is a link to one that I have found:
this tutorial also goes through using the Import function.
Your Host should have a control panel that you can access to create and manage the MySQL Database on your remote site. Access the control panel to create a new database, and then launch PHPMyADMIN from the control panel to manage it, you will need to use the import feature to import the database file that you exported from your local system.
you will now need to edit the Connection/PowerStoreConnection.php file to connect to the remote database sever, the details for this should be available through the hosts control panel, if you need assistance accessing the control panel or finding the connection details, contact the host and they should be able to guide you.