You have to be the admin of the group to be able to make these changes.
Go to "My Groups" via the drop-down menu in the header at the top right. Click on the desired group from the group overview.
At this point you should be able to see the list of the group members. Here, click on "+ Add Members".
Now you can look for individual users by searching for their name via the search bar or by scrolling through the list. You are able to add multiple users at the same time.
Suggestion: If you want to add several students in the same class, you can enter the class directly using the search bar. You will then only see students of this class (and the corresponding parents of the students).
Mark the users you want by tapping the circle next to their name. Once you have made your selection, you can confirm it with the red arrow in the footer.
Accidentally clicked on a wrong user? No problem!
Look at "How do I remove users from a group?"