When using a web browser you access your Smoogle account using your University Directory ID and password as described here. However if you're not using a web browser (e.g. perhaps using are using a smartphone app, an email client such as Thunderbird or Outlook) then you need to set a Google password on your account that you use along with your Smith email address to login.
Normally you'd use your UM Directory ID and password when accessing on the web, but if for some reason (e.g. an internet outage or other technical issue occurs) you are unable to authenticate with your Directory ID, you can use this link below to login to Google Apps using your Smith email address and Google password.
Once you're logged in, just choose the Google service you want to use!
Note that if you login using this method and check the box to Stay signed in then you must be aware that closing your web browser will not log you out. You must manually sign out by clicking your account photo or email address in the top right hand corner and selecting Sign out. See this article from the Google support site.
Note to Alumni
When you graduate from the Business School the University generally keeps your University Directory ID active for 270 days (~9 months), after which your University account is disabled. If you had been using your University Directory ID to login to your Smoogle account via the web you will need to switch to using the alternative login prior to that cut off date.