Go to Settings -> School (the same screen a family calls "Family" - the label follows your account, the destination doesn't change). Use the invite form: first name, last name, email.
Admin or Member
A school account gives you a role choice when you invite someone, defaulting to Member:
Admin - full access across the whole school: every class, staff management, billing, reports.
. Nothing else needs to be set up first; assigning them to a class is what grants access, not a separate permission step.
What a teacher sees before being assigned
Nothing. A Member who hasn't been assigned to any class yet sees an empty class list. Trying to open a class directly by its address behaves the same as that class not existing at all, rather than showing a permission error - a deliberate choice so an unassigned teacher can't even confirm which classes exist.