You will authenticate your G Suite account like you do your Office 365 account, with your full EKU email address and password:
Open www.google.com and be sure you are logged out of any other Google accounts by clicking the icon in the top-right corner and choosing the Sign out button. If you do not have that, you are not currently logged into a consumer Google or G Suite for Education account.
Now click the G Suite Apps icon in the top right and choose the Drive icon to login (this is not your only G Suite for Education app but it is a major one for collaboration). NOTE: You will not have access to all apps on this list, for example, Gmail is not available.
Now on the Google login screen, type your complete EKU email address then click the Next button:
You should be redirected to the EKU Authentication page where you will use your full EKU email address and password as login credentials:
The first time you login you will see a Google Terms of Service (Welcome to your new account) page. After you read this, click the Next button:
The first time you login you will see your G Suite for Education Drive with a tip overlay. You can move through those by clicking the blue right arrow or click the X to close:
Now you will see your basic Drive page. There will be a Getting Started how-to PDF to get you started using this service: