This page explains how to find the Tah Muhl shrine and solve the "Passing the Flame" puzzle.
How to Find the Shrine
Glide south from Eldin Tower and you will go over Lake Ferona, a hot spring. If you have not increased your Stamina Wheel, try to land on a rock in the lake. Just south of the lake, there is a valley between two peaks. Go southeast from there to find Tah Muhl Shrine hidden in the hills.
How to Solve the Shrine
You will need a source of fire to complete this shrine, such as fire arrows, or wood and flint, or a flame weapon.
There are dry leaves on the walls in this room. Burn the leaves across from where you entered to reveal a new area. (If you have a torch, you can light it on one of the torches down the hall from where you entered.)
Go through the opening that you revealed. You can see a treasure chest on top of some crates. The chest is made of wood, so if you burn the crates, the treasure chest will also burn. You can hit the crates with a heavy weapon to get rid of them without burning the chest. The chest contains an opal.
There is another treasure chest in this area, behind some leaves next to the hole that you entered the room through. Burn the leaves, then jump up onto the crates and jump to the chest. It contains a Cobble Crusher.
There are two additional treasure chests beyond a locked door. You have to burn the leaves on the wall to the left of the locked door, which will burn the treasure chest on the left, revealing the small key that was in it. Use Magnesis to pull the key over the bars (it can't fit through the bars) and then use it to unlock the door to open the final chest in this shrine, which contains a ruby.
Finally, burn the four crates that are stacked under a raised walkway near Tah Muhl. This will lower a ramp that you can walk up to check on Tah Muhl and get a Spirit Orb.