After you complete your first shrine trial, the old man teaches you how to find the next shrines.
How to Warp
When you leave the shrine, the old man will meet you. He tells you to find the other three shrines in this area, and recommends looking from a high point. He also explains how to warp back to locations that you have been to: press Select to open the Sheikah Slate map, and select a glowing blue spot to warp there.
How to Use the Sheikah Scope and Pins
Warp to the top of the tower and talk to the old man. He will tell you about the Sheikah Scope. Push the right control stick (like a button) to use the Sheikah Scope. Then look around. When you are looking at something that you want to go to, move the camera so that the little dot in the center is pointing at it, then press A to put a pin there. You can open the Sheikah Slate map to edit pins.
When you have pinned something, the pin will be visible on your minimap, making it easy to go in the right direction. But before you go to any pin that you have placed, you should also look from a high vantage point to figure out how you will get there. Otherwise, you might find a tall cliff, a wide river, or some other obstacle blocking your path.
The three shrines are all in the mapped area, not in an uncharted area. If you put a pin on something in an uncharted area, you are not supposed to go there yet, so try looking again for the nearby shrines to pin.
Also, pins will only be glowing if you look through your Sheikah Scope, so if you see something glowing when you are not using the scope, it's not one of your pins.
One of the shrines is to the west, one is to the south, and the other is about halfway between those two.
One of the shrines is in the eastern part of the Great Plateau area, in the Eastern Abbey. This one is easier to reach than the other two, so warp back to the Oman Au Shrine (and use Magnesis on the water near the shrine to find a couple of treasure chests), then go southeast toward the eastern shrine.
Avoid the Robots
In the Eastern Abbey area, there are some dead robots that you can search for ancient screws and springs, but beware: some of the robots in this area still work and can shoot beams at you. Shooting them in the eye will stun them, but not for long. To reach the shrine without encountering enemies, go around the east side of the Eastern Abbey area and climb the wall that is east of the shrine building.