To add a contact to a group:
var
gc: TGContact;
gcg: TGContactGroup;
gc := TMSFMXCloudGContacts1.Contacts[0];
gcg := gc.Groups.Add;
gcg.ID := TMSFMXCloudGContacts1.Groups[0].ID;
TMSFMXCloudGContacts1.Update(gc);
This is demonstrated in the GContactsDemo application.