First, click your name in the upper right and go to Staff/Classes.
Next, click the +Add Students button to invite a new staff member to the school. If you are a School Administrator, you also have the option of adding other School Administrators.
Then, put in the email address of the teacher you want to invite.
Alternatively, you can go down to a classroom and click Manage Teachers and click the New Teacher button.
There is also the option to add a staff member as a Class Admin. However, this role is for staff members who will only take on an observatory role like a substitute teacher and will not have the regular permissions that a staff member in the Teacher role would have.