Under Playlists / Saved Playlists, there's an area for "Playlist Files on Disk". I'd think that's where I would find a playlist that I saved on disk. But all I see is the "Playlist Files on Disk" bar. Clicking on it does nothing. So how can I retrieve my playlist from disk (so that I can edit it).

'Playlist Files on Disk' refers to playlists which have been saved into Amarok's playlist directory, which is ~/.kde/share/apps/amarok/playlists (may be .kde4 on some distros). You can add playlists there and they'll be detected at least on next start, and possibly on collection updates (I don't use them myself, so I haven't tested). Alternatively, you can use Amarok > Play Media or Playlist > Add Media to open playlists from anywhere on disk.
Playlists can be saved to Amarok's database or to the playlists folder with the save icon at the bottom of the playlist, or saved anywhere on disk with Playlist > Export Playlist As.

The save icon at the bottom of the playlist seems to save the playlist in the Amarok Database rather than in ~/.kde/share/apps/amarok/playlists . So I still don't see how playlists can ever get there other than by using the export function and naming that directory explicitly -- which seems awkward at best.

The down arrow in the corner of the icon means there's a menu attached to that icon; click and hold and you get a menu with the option to save to the database or the disk.

I don't see a down arrow -- but clicking on the icon and holding brings up a menu showing the two places to store the item: Amarok Database and Playlist Files on Disk. Hardly obvious -- but it solves the problem.