You can connect to SQL database hosted on remote machine. To connect to the database, hosted server should allow remote connections. Also, you should have following permissions for connection.
1. Connect to SQL server.
2. Connect to database, read and write(if needed).
The SQL server listens on 1433 port (a default port).
Install SQL server management studio to view the databases. The SQL server client allows you to backup/restore the databases with pretty simple steps.
Look at following MSDN articles.
How to: Back Up a Database (SQL Server Management Studio)[
^]
How to configure SQL Server 2005 to allow remote connections[
^]