Who knew it would be so tricky?! At the moment the page on which to order films online seems well hidden. Why would they keep it a "secret?" I have no inside knowledge, but here is what I think. FamilySearch has been rolling out online ordering in stages. As an area converts to online ordering it is responsibility of the Family Research Centers to teach the patrons in that area how to do it. At the Ann Arbor branch (housed in Saline) we recently had our training session and we explain and demo to patrons as they come in to order. Now that the whole United States has online ordering the instructions (and a link to the page to start the order) will probably appear in the next update of the FamilySearch.org site.
In the meantime, here is the link https://www.familysearch.org/films/ -- if you don't have the link handy, just /films at the end of the basic url.
And here are the instructions, posted courtesy of the Genealogical Society of Washtenaw County