This is done by showing a dialog containing an <input type="file">
through which the user can 'upload' a save file - though, of course,
the 'upload' doesn't go to any HTTP server, but only into the mind of
the Javascript running in the same browser.
It would be even nicer to support drag-and-drop as an alternative UI
for getting the save file into the browser, but that isn't critical to
getting the first version of this feature out of the door.