Start from the Gerudo Tower. You're going to be heading slightly northwest of here.
This is where you want to go – it's in a canyon, surrounded by outcrops, midway between the tower and the Yiga Clan hideout. Set a marker on your map around here and you should be able to find the pedestal you need to activate to reveal the shrine.
Once you find the pedestal, pay attention to your surroundings. There are four mineral deposits scattered around it, as well as a stone tablet with a message on it.
"Offer a shining blue stone," it says. Sounds like a Luminous Stone – and there's at least one in each mineral deposit here. Remember this, because there are a few quests and items in the game that require Luminous Stones (there's a quest in Zora Village, for instance, that will let you trade them for a diamond).
Place a Luminous Stone at the center of the pedestal and the shrine will reveal itself before you. Time to get to work!
The clue for the Sho Dantu Shrine is "two bombs." This will help you with the last puzzle. There are no Guardians in this shrine, so you can relax and have fun in here.
There are entrances to your left and right as you start; the one on the right is sealed off for now. Access the one on the left by blowing up the crates blocking it with a bomb.
In here, there's a pad that launches whatever is placed onto it into the air every few seconds. Put a bomb on there and detonate it in the air as it reaches the cage above. Enjoy the fireworks – they've just opened up that door to the right back in the main chamber.
Head in here and you'll find another pad, except this one you'll need to activate manually.
Head behind and you'll find a switch. Hit it once to make the pad shoot up, making any bomb you've placed on the pad fly into the air. You'll have to guess on this one, but detonate the bomb about a second after you hit the switch and you should unlock the final chamber. If you miss the timing, hit the switch to lower the pad, then go back and put another bomb on there to try again.
This final chamber is where you'll need to use your two bombs – one spherical bomb, one cubed bomb. Note the two pads either side of the entrance – you'll need to stand on one of them soon.
There are pads on either side of the room that periodically shoot out. Equip your square bombs, and put it on the right pad. The bomb will be fired into the cage on the pillar between the two pads, where the switch is.
Put a circular bomb on either of them and it will be passed back and forth between the two pillars indefinitely. Throw a bomb on there and let it go.
Go and stand on one of the two pads near the entrance and detonate the square bomb. The platforms will raise up, but the entrance to the throne will be closed off. Watch your circular bomb now, and as it passes over the cage, detonate it. This will hit the switch, lowering the pads that brought you up there and opening the door.
You did it! Collect your Shadow Orb, and remember this site as the place to come back to later for Luminous Stones once the deposits regenerate.
Don't miss our other handy guides for Breath of the Wild.