This page explains how to start and complete the The Ancient Rito Song shrine quest.
How to Start the Quest
After you free Divine Beast Vah Medoh, talk to Bedoli at Rito Village to start the quest. She can be found on Revali's Landing (the big ledge in the eastern part of the village) during the day.
How to Complete the Quest
After Bedoli sings the song,
go west and go clockwise on the walkway until you reach the quest destination,
where you will find Laissa. Talk to her and recite the song:
To the south, across the lake, there is a shrine pedestal. Float onto it and make a campfire on top of the pedestal, then sit until noon. Re-light the campfire if it went out (or light a torch on top of the pedestal), then when the heart-shaped light hits the pedestal (at about 12:35PM), the shrine will appear.
Check the Bareeda Naag Shrine page for details on completing the quest.