You can tap on the Invite button under the name list in your Clique to send an invitation to your friend. They will receive the invitation in the mail menu of the Clique window.. When they tap to accept your invitation, they will become a member of your Clique.

If the "Invite" button doesn't appear, it means that either the selected friend is already in your Clique or they haven't reached the minimum required level to join Cliques.

You can also accept Clique invitations from your friends. You can check them by tapping the Mail icon at the bottom left of the Clique window.