I have taught our ward's Priesthood Preparation class in the past, and one of the lessons in that class is "The Apostasy". I think that designation is a bit misleading, as I believe "The Apostasy" was not a one-time event that lasted for hundreds of years.
When I discuss "The Apostasy", I try to address the foundation concept of apostasy as a historical process and condition of every culture since Adam, then position "The Great Christian Apostasy" as just one of many throughout time. If I'm talking to a Priesthood Prep class, for example, I start with the Great Spirit Apostasy (the War in Heaven), move to the Edenic Apostasy (The Fall), discuss the First Great Mortal Apostasy (from the early patriarchs to Abraham, Isaac and Jacob) and detail at length the Great Jewish Apostasy of the extended silent heavens (Malachi to John, the Baptist) - before even beginning to address the Great Christian Apostasy. I then move to the concept of "short term apostasy" so prevalent in the Book of Mormon and individual apostasy that always is current - and talk about how easily such "individual and institutional apostasy" can rear its head even in the Restored Church. I point out that the Book of Mormon explicitly describes the on-going effects of apostasy (both the lingering effects of the "incorrect traditions of our fathers" and of the doctrinal misunderstandings new converts bring with them when they are baptized) within the LDS Church itself in the final stages of the allegory of the Lord's vineyard in Jacob 5.
I think this approach is the best way to frame apostasy for those outside our church, since Protestants and Catholics and those of other religions usually understand the basic, historical concept - even if they don't accept our specific view or the solution of The Restoration.