If you can please, do get info about how the Orthodox Churches do it. Thank-you and God Bless.
The Orthodox churches—they are schismatic, don't forget—allow divorce and remarriage (at least second marriages), and therefore are not proper models of how we as Catholics should handle annulments.
It’s my understanding that it becomes an issue for the Orthodox Church if an individual seeks to be married again after a previous marriage ends (otherwise, there isn’t a sacramental question). The bishop of that Diocese will receive a letter from the priest who is to conduct the wedding of that individual and will then either grant or deny the request for a second marriage to be performed.
I understand that the second marriage ceremony is actually different from the standard and includes prayers of repentance for the first marriage.