To me the top of the cover is the end without buttons, so I start by inserting the top corners of the duvet in the top of the cover, turned right-side out, which was the way we always used to do it in Denmark.
The younger members of the community think outside in is easier - I have tried it and found it even more difficult and it offends my sense of good housekeeping to put anything away outside in!
I can no longer shake a duvet and its cover without hurting my shoulders, so after the top corners are in place I put the whole caboodle across the bed and work the lower corners into place in the cover, taking care that the lenght-wise edges of the duvet don't roll in but are against the edges of the cover.
If DH hadn't been born and bred in Denmark, where top sheets are not used, I would long since have reverted to top sheets and only changing the duvet covers once a month or so.