On The Mobile App:

Tap on the child photo at the top of the screen, then tap on the Add Parent / Caregiver button under the Caregivers section. Enter the parent email address. 

On the Web App:

Click on the Settings > Childcare Settings > Children > [child name] > Add a new parent/caregiver. Enter the parent email address. 

An invitation email will be automatically sent to the parent with an invitation code. The invitation code is unique to each parent.