Create Sql Server Backup on Local Machine -

I am using SQL Server Management Studio running on my local machine.

I use a studio to create a remote box (database engine) and a database backup that is saved on a drive on the remote box.

How can I save a backup to the drive on my local machine?

Look at the section for sharing a network, for example:

  Backup your database to database DISKS = '\\ some michine \ backup \ yourDatabase.bak';  

Backing to a file on a network
To access a remote disk file, share it for SQL Server, SQL Server Service account needs access to the network share in it to include the necessary permissions for backup operation to restore the network and restoring tasks to read from it. The availability of the network drive and permission depends on the context that the SQL Server service is running:

• When a domain user account is running SQL Server, to back up a network drive , The shared drive should be mapped as a network drive in that session, where SQL Server is running. If you start Sqlservr.exe from the command line, then SQL Server sees any network drive mapped to your login session.
  
• When you run Sqlservr.exe as a service, SQL Server runs in a separate session that has no relation to your login session. The session that runs a service can have its own map drive, although this is not usually the case.
  
• You can connect to a network service account by using a computer account instead of a domain user. To enable a backup from a specific computer in a shared drive, provide access to the computer account. Unless the Sqlservr.exe process is writing backup, it is irrelevant whether the user sending the backup command has access.