Shae Mo'sah Shrine
If this is one of your first Shrines in the Eldin region (particularly surrounding Death Mountain), prepare for a lot of Shrines that utilize fire. This Shrine is comparatively short and simple to some of the other ones nearer to Death Mountain and as such is a great way for you to get acquainted with the types of puzzles you will find endemic to this area!
You need to activate the switch to open the gate. Then shoot down the torch to burn up the vines and wooden shelf holding a barrel. The barrel will fall down, and you can then place it on top of the floor switch.
You could also use a well-timed Bomb, or simply use Stasis on the switch after standing on it.
In the next room, turn left and open the chest for a Stone Smasher, a powerful but slow weapon. Ignore the wheel for now and defeat the Guardian Scouts up ahead.
Open the chest in the corner of the room for a Ruby. Run up the nearby ramp and turn right. Then go up another set of stairs. Right behind the floor switch that you can see is another chest containing 10 Ice Arrows. Lovely.
Step on the switch you just saw earlier to drop a torch. Use Magnesis to grab the torch and swing it over the vines, setting them on fire. Now follow the ball that is allowed to roll around the corner. Step on another floor switch to open a gate blocking its way. The ball will turn the large wheel we saw earlier, opening up yet another gate.
Open the chest to your right immediately after entering the gate for a Small Key, a Shrine-specific item that will let us finish the puzzle. Go up the ramp, drop down, and head to where you previously passed by a locked door.
Open the door and step on the first switch you see to drop torches and again, use Magnesis to swing the torch and burn up the vines. Then place the barrel on the switch, just like we did when we first entered. Again, you can use bombs or Stasis here as well. Now you can claim your Spirit Orb.