If your hosting company has provided you with a database then they should be able to help you with the connection string.
Most times there is a control panel for the hosting where you can create a database and a user and it will then show you the server name and from this you can create a connection string.
I recommed that you start with a clean database on your host. If you want to use the database you already created on your local machine then you need some way to restore it on the hosted server. Again that depends on your host.
Hope it helps,
Joe