Here is how to silently install SQL Server Management Studio:
- Download the installer from https://msdn.microsoft.com/en-us/library/mt238290.aspx
- Run the silent installer using the following command line:
SSMS-Setup-ENU.exe /install /quiet /norestart
How did you figure out what switches to use ? By running
SSMS-Setup-ENU.exe /?
you will be presented with a helpful dialog documenting the supported switches.

Other supported modes are uninstall, repair, and layout. It is also possible to set the location of the log file created by the installer.