To get the quest, you will have to go to Tianqiu Valley, in to the ruins, and interact with the stone tablet that's just behind the mechanism with a crystal on it. Make sure that you have a character that can light a fire, and the main character with Geo element for a platform boost, you'll need them to clear the rooms. Venti can also work instead of main character Geo.
In order to power the device, you have to get the energy from the 3 rooms on the sides, and another one just behind it. The room on the left simply requires you to defeat monsters within a certain amount of time challenges. The room behind the device is some platforming section, where you will have to use some height boosting ways, like Geo elemental main character or Venti. Both of them are somewhat straightforward, but the room on the right can be somewhat confusing.
The first floor is pretty simple, lighting one of them will light 2 others in a triangle direction. So all you need to do is light one with a red on the bottom, and the other one with no red.
The next one works similarly. Which one you light first doesn't matter since they're all connected unlike the first floor. It's probably easier to look at a youtube video than to explain it here, but the way you light all of them is by reducing the number of lit torches to 1 first, then go to the left/right twice of the remaining one that's lit and light it, then the remaining unlit ones should be clear.