Talk to Nanna who got injured. She notices your Sheikah Slate and suggests you go see Lady Impa who lives at the bottom of Lantern Falls. Get off your horse, then start to go around the village. You can find a Farming Hoe near the entrance. Talk to Olkin in the pumpkin field who tells you about the Yiga Clan (the ones who sworn loyalty to Ganon) and gives you a Fortified Pumpkin. A bit below, you are called out by Lasli in front of the shop "Enchanted". Enter the shop and look at the available clothes. On the counter, read the book "Rumor Mill", a collection of rumors. Get out, go left and go near the two men in front of a house. When they see your Sheikah Slate, they let you through. Once you've met Paya, get into the house and speak to Lady Impa. She tells you about the past and about a message left by Zelda. Tell her that you're ready and she will tell you the legend:
The history of the royal family of Hyrule is also the history of Calamity Ganon, a primal evil that has endured over the ages. This evil has been turned back time and time again by a warrior wielding the soul of a hero, and a princess who carries the blood of the Goddess. With the passage of time, each conflict with Ganon faded into legend. So listen closely as I tell you of this "legend" that occurred 10,000 years ago. Hyrule was then blossoming as a highly advanced civilization. Even the most powerful monsters posed little threat to the denizens of the realm. The people thought it wise to utilize their technological prowess to ensure the safety of the land, should Calamity Ganon ever return. They constructed four mechanical wonders that came to be known as the Divine Beasts. They also built a legion of autonomous weapons called Guardians. The Divine Beasts were piloted by four individuals of exceptional skill from across the land. And thus, the plan to neutralize Ganon was forged. Upon Ganon's inevitable return to Hyrule, the princess and the hero fought alongside these four Champions against this ancient evil. The Guardians were tasked with protecting the hero as the Divine Beasts unleashed a furious attack upon their terrible foe. And when the hero wielding the sword that seals the darkness delivered his final blow... The princess used her sacred power to seal away Calamity Ganon.
But a hundred years ago things didn't go as they were expected to. Zelda is now asking you to set the four Divine Beasts free. Daruk, of the Goron tribe, used to operate the Divine Beast Vah Rudania. Revali, of the Rito tribe, used to operate the Divine Beast Vah Medoh. Mipha, of the Zora tribe, used to operate the Divine Beast Vah Ruta. Urbosa, of the Gerudo tribe, used to operate the Divine Beast Vah Naboris. Impa suggests to go meet the four tribes in the various areas of Hyrule. These tribes' chiefs' villages are shown on your map. She says that your Sheikah Slate is incomplete and that someone at the Research Lab in Hateno Village may help you.
Before you go, you can read the Journal of Various Worries left of the door, the source of side quests. Outside Steen gives you a Swift Carrot. Next to him is a vegetables and fruits shop. Get into the inn in front and talk to the owner and if it's night time, with the client. During daytime, this man is painting in the middle of the village. Next to it the another shop sells Wooden and Fire Arrows.
Go back to the entrance of the village where you're coming from and go up the left path. (One of the cuccoos is there.) On the right is another shrine. Place the Sheikah Slate on the terminal and get in...
Ta'loh Naeg Shrine - Ta'loh Naeg's Teaching
Open the chest on the left which contains an Eightfold Blade as well as the one on the right which contains a Shield of the Mind's Eye. Then go to the centre to get a fighting lesson! Perform some side hops as shown, then when the Y button appears, deliver several sword blows. Then you have to perform a backflip right before you're touched, then quickly counterattack. Then it's the Perfect Guard and finally the Charged Attack. Once you've destroyed this guardian, pick up the Guardian Sword and one or two Ancient Screws/Gears. Climb the steps, pick up the Opal in the chest, then look at the Sheikah symbol, and the monk will give you another Spirit Orb.
Go back to the village. Pray to the goddess if you have at least four Spirit Orbs, then go back to the Dueling Peaks Stable. On your way, next to the Kakariko Bridge, you can meet a traveler who will ask you to join the Yiga Clan founded by Misko. Bad news, he's an enemy. Fight or avoid him, then once you've reached the stable, go eastwards.
Once you've passed Fort Hateno, you spot a house on the right in the forest. Get in and talk to the archaeologist Calip: "When a dark light resides in the cursed statue's eyes, pierce its gaze to purge the seal from the shrine". If you call him Doctor Calip, he'll give you a mission. (If he's not in, you can read his book.) Keep going east. When the path is splitting, if you have spare time, go left. You end up in a clearing with lots of small statues. Pick up an Emblazoned Shield on the ground. At night time, one of those statues has purple eyes. Shoot an arrow at it, which will cause a shrine to appear! Place the Sheikah Slate on the terminal and get in...
Kam Urog Shrine - Trial of Passing
Go down the slope, go ahead, climb on the little ledge and look at the two gears. When the biggest piece gets in front of you, use the Stasis Rune on the gear on the right, then move to the left of the big piece. When the Rune isn't active anymore, climb on the piece and jump on the gear. If you want an Opal and a Soldier's Spear, freeze the gear you're on, jump (with the X button) to the chest on your level and open it. Then turn around and look for another chest on a rotating piece. When the chest is in front of you, freeze the right gear and fly to it. Open it, jump down, then come back onto the horizontal gear. Look on the right of the second gear and freeze it when a piece is horizontal to allow you to go to the far right corner. Then jump on this piece, then on the next one which is still. Now jump on the gear, let it take you higher and jump on the still part. Climb the still steps, then use the Stasis Rune on the gear below when the stairs-piece is in front of you. Climb the steps to the top, go left and look at the Sheikah Symbol. The monk Kam Urog gives you another Spirit Orb.
Then, go back to the place where the path was splitting and go left (eastwards). Further you can find some cracked rocks on your left that you can blow up in order to find some Amber in a chest. Just after crossing paths with some Bokoblins, cross the river on a narrow passage southwards and go on this way towards the tower.