Members of your class can be added to a class or invited through the "Students" tab. After signing into Google, navigate to classroom.google.com and click on the "Students" tab.
To invite students to your class choose the blue "Invite" button in the top left of the screen. You can filter the potential guest list by clicking on the "My contacts" button and then choose from various groups in your organization. The "Directory" will be the most comprehensive but this will also depend on how your domain admin has set these groups up.
Additionally, if you know specific names of students you wish to add, use the search box in the top right to key in their names, and then check the box next to each student you wish to add.
Once you add the names of the students you wish to have join your class, Click on the blue "Invite Students" button.
These students will show as "Invited" until they navigate to classroom.google.com and accept the invitation to join.