This is how I do it:
First I export an SQL file of the entire database (except orders and orderdetails). I do this using PHPMYADMIN. I open the database, hit the export tab, select SQL, and save it under the name given to me by my provider.
Then I log into the provider's PHPMYADMIN. They will have to give you a login name and password. From there I import the SQL file I just created.
Hope that helps.