There are 2 ways you can get the Classroom app and these depend on how your school has set up its device management.
What is Device Management?
Mobile Device Management, or MDM, is the system that your school's IT Admin uses to manage all their devices, including giving you access to all the apps you need to work and making sure these are updated. Some schools will only use MDM to track their fleet of devices, but not have their devices 'managed' meaning that you can sign in with your own Apple ID, and freely download apps from the App Store. Some schools or institutions will fully manage their devices, meaning that you will be using a Managed Apple ID, assigned to you by your admin, and cannot download apps from the App Store.
App Store
If your school is not using Managed Apple IDs on their devices, you will be able to download Classroom straight from the App Store. If you do not see the Classroom App in the App Store, you may need to contact your Admin to make sure your Apple ID and Goodnotes Account are registered in their Portal.
Via MDM
If your school is using Managed Apple IDs, you will not have access to the App Store so Classroom will need to be pushed through to your device using your school's MDM. If you have not received the app and can't install it using your Self-Service Portal, or if your school MDM does not use Self-Service, then you should contact your Admin and ask them to deploy the app to your device.