The Ceremonial Song
To unlock this Shrine Quest, you have to have first completed the main quest "Divine Beast Vah Ruta". Learn more about it here.
Speak with Laruta, a small pink Zora girl. She will sing you a song that has great historical meaning to the Zora race. The lyrics actually are hiding a Shrine. Once you have heard this song, the Shrine Quest will be added to your Adventure Log.
Go talk to Trello next, who will talk about a Ceremonial Trident being needed for an upcoming festival. Trello can be found on the bridge west of the Zora's Domain. There's a problem, unfortunately. He dropped it into the water and can't find it.
While facing Trello, jump off the right side of the bridge and then Paraglide to the nearest land you see. Use Cryonis to then go back into the water to your right, towards the bridge you jumped off of.
Switch to the Magnesis rune on your Sheikah Slate and start scanning the water for the missing trident. Once you are close enough, pull it up and equip it. You will need it, so if your inventory is full you have to let go of something.
Speak with Trello again and he will let you keep the trident. Head to Veiled Falls which is marked on your map with a yellow dot (if you set this Shrine Quest to show up on your map).
You will see the glowing orange platform that is characteristic of a Shrine waiting to be unlocked. Swim up the waterfall using your Zora Armor and then once you have deployed your Paraglider, fly back down to the platform.
Before you can land on the platform, press [Y] with the Ceremonial Trident equipped and Link will attack from the air, driving the trident into the platform. You just have to attack the platform. If you miss the center, that's okay.
Done properly, the platform's color will change to blue and the Dagah Keek Shrine will appear, marking the end of this Shrine Quest.