After you help investigate the mystery in the Depths for Josha, you can talk to Robbie to start this side adventure.
Quest Location
You can begin this quest after you complete A Mystery in the Depths. To start this quest, talk to Robbie at -0248, 0134, 0018 in Lookout Landing.
Reach Hateno Village
To reach Hateno Village from Lookout Landing, exit the town by the east exit. At the first split in the road, go straight, and at the next split, go straight again. At the third, go left (the path that goes northeast). This will lead you across Rebonae Bridge. Just after the bridge, take the south path when the path splits. This leads you to Wetland Stable. You will find Tukarok Shrine south of this stable.
From the stable, go southeast along the road. Don't go to the Lanayru Wetlands east of the path. Take the road that goes southeast past the Wetlands. You will find Morok Shrine to the right of the road as you go.
Eventually, the path will take you through Kakariko Village. You can find Makasura Shrine on the hill southwest of the main part of the village.
Continue east through Kakariko, and you will eventually go southwest on Kakariko Bridge. Keep going south to find Dueling Peaks Stable. You can look west from the stable to see Eshos Shrine on the hills.
Then go north from the stable, and when the path splits, go east. You will eventually reach Fort Hateno, but beware: Monster Forces—the Marauders of Necluda—are guarding the wall. If you have completed Bring Peace to Hyrule Field! and there hasn't been a blood moon since then, Hoz's monster-control crew will be here at Fort Hateno and you can help them defeat the monsters. Otherwise, you can look for a piece of rubble that fell from the sky, then stand on it and use Recall, then glide down from it to go past the monsters.
After you make it past the Monster Forces, follow the road beyond the Fort Hateno wall. Each time there is a fork in the road, keep going straight. This will lead you to Hateno Village.
In the village, you will find Zanmik Shrine.
Go to the Lab
Continue going east on the road through town, and it will eventually lead you up to the lab on the top of the hill. Go inside. (If it's locked, you need to complete A Mystery in the Depths first, then talk to Robbie in Lookout Landing.)
In the lab, talk to Robbie. He will add the shrine sensor to your Purah Pad. It will detect the shrine in the cave beneath the lab, unless you have already found it. If not, you can find Retsam Forest Cave's north entrance at the base of this hill, on the north side (3750, -2028, 0191). Inside, you find Mayahisik Shrine.
Afterward, Robbie will put up a poster with instructions on how to use the sensor. This completes the Hateno Village Research Lab quest. You can now talk to Robbie again to learn how to add several new features to the Purah Pad.
Be sure to ask about the Travel Medallion feature, because this will add the Hateno Lab as a teleport location to your map. This starts the side adventure Presenting: The Travel Medallion!
If you ask about Hero's Path Mode, Robbie says that you need to visit at least 15 shrines before he can unlock it. This starts the side adventure Presenting: Hero's Path Mode! When you complete this side adventure, Robbie will put up a poster with instructions on using the feature.