For a very simple backup: BACKUP DATABASE [DatabaseName] TO DISK = '\\archive1\sql$\ArcGIS\DatabaseName.bak' The SQL Server Engine service account would need permissions to read/write to that particular directory. Reference:
https://msdn.microsoft.com/en-us/library/ms186865.aspx Hope that helps!
You will have to make sure that account that SQL Server is operating as has permissions to write to the share/folder in question. Then create your script for the backup to occur, putting the path in the TO DISK portion of the code.