Where in the Zelda timeline does Skyward Sword fit

You need to talk to the professor outside the upper exit of the academy, then head to the spot marked Plaza on the map, which should trigger a cutscene.

There are more steps to it after that, but I'm not sure if you want more than that or not.

You can only access the Moonlight Merchant toward the end of the game after you completed the Hero Song.

At this point, the monsters will leave the Waterfall Cave completely and you will find the butterflies inside at night.