At the place, create a database (with the same name if you wish) and give it the same credentials as the database at the old place. Create a user (with the old credentials) and assign it to the new (empty) database. Then use phpMyAdmin to import your old database into the newly created (but empty) database.
Look at the database user name to make sure all is correct (it might have a slightly different prefix to the user name or database).
Then make sure that your wp-config.php file has the proper credentials (which might be slightly different due to naming conventions at the new place).
Make sure the wp-config table has the proper URL for your new place. And make sure that DNS for your new place is set properly for your domain name. (A CMD prompt where you type in NSLOOKUP example.com should give you the IP address of the new place. If it doesn’t, clear your local DNS cache with a IPCONFIG /FLUSHDNS command.)
At that point, assuming that you have copied all of your WP files (core, theme, plugins), you should be able to access. Double-check your wp-config.php file to ensure proper credentials and database names (with any variation in naming the database/user).