After you arrive in Zora's Domain, you wash the sludge-covered statue, and you are asked to meet Sidon on Ploymus Mountain.

Talk to Yona

Before you go up the mountain, go slightly southwest from the statue of you and Sidon, then go up one of the large curved stairs. It leads up to the area with the throne room. Instead of going into the throne room, go to the area behind it, where you will find Yona. Talk to her to start the quest Restoring the Zora Armor.

Go to Ploymus Mountain

Your next task is to meet Prince Sidon on Ploymus Mountain. To get there, start by visiting the Upland Zorana Skyview Tower. One way to get there is to cross the northwest bridge of Zora's Domain, then follow the path southwest. It leads to Ralis Pond, where you can gather many materials. Then go northwest from the pond to find the entrance to the cave Upland Zorana Byroad. This cave leads you to the Climbing Boots, and gives you an easy way to reach Upland Zorana Skyview Tower.

After you throw a Splash Fruit at the tower entrance, use the tower to map the area. Then skydive to Prince Sidon's location, which is marked on the map. Talk to him and there will be a cutscene.

Talk to Jiahto

Go northwest to Toto Lake, and talk to Jiahto. This begins the quest The Broken Slate. Go slightly east from Jiahto, then go slightly north along the shore of the lake, and you will find the broken slate covered with some sludge. Throw Splash Fruit at the sludge, then use Ultrahand to move the broken slate in place on the wall near Jiahto. This begins the quest Clues to the Sky.

Report to Sidon

After you complete Clues to the Sky, talk to Sidon. You will find him talking to Yona. During the cutscene, an enemy will appear. You and Sidon will fight the Sludge Like.

After the battle, be sure to open the chest that the Sludge Like dropped, to get a Royal Claymore.

Go to the Pillar of Light

Then go southwest to the statue of Mipha. From the southwest edge of this cliff, you can glide down to the stone column where the quest destination is. Sidon is standing on the stone column, looking at the pillar of light in the East Reservoir Lake. Talk to Sidon and he will open a path for you to dive into at the pillar of light.

After you glide to the pillar and dive into it, you end up in a cave. Go forward and look for a rock that is blocking some water. Break this rock (you can use a bomb flower, or a rock hammer, etc.) and the water level will rise. Go north to the new area and you will find the Ancient Zora Waterworks.