Go to Tools > Online Web Registration > Settings and scroll down to the 'Class Search Settings' section. Set Allow Waitlist When Class Full to "Yes" and set What Impacts the Number of Class Openings? Waitlist row to "Yes" for Online Registration and Quick Registration. Remember to Save Changes.
The Allow Waitlist When Class Full setting affects all online registrations - Online Web Registration, Class Listings Tables, Quick Registration, and the Parent (Customer) Portal.