So here are some pointers for the novice exporter, from a mostly novice exporter.
First, it is only a one-way sync, exporting your LDS calendar to some other application or file.
I believe that the export function will export the combined details of all the calendars you are subscribed to, without regard to which of those you might have checked to view at the time you export. If I am wrong, someone please clarify.
From the calendar page, select 'settings', then 'Sync'.
Then you'll have three options: Google Calendar, Microsoft Outlook, and Apple iCal.
Since I think you were asking about iCal, select that one. That will yield a URL something like this:
http://lds.org/church-calendar/services ... xxxxxxxxxx
(where the x's are digits.)
Now, if you want to get the actual iCal file, paste the URL in the address bar of your browser, and your browser should help you download the file.
But the file alone is not so useful as it is encoded. You need to put it into some kind of calendar application, perhaps using that application's 'import' function.
Some calendar applications have a sync function where you can enter the URL right into the application, and it will download and populate its calendar with the info from the URL.
I hope this helps.