Go to Eldin Volcano. After a short cutscene, you'll be in a cell. Break around some pots for hearts, and after a bit, a Mogma will appear giving you back your Mogma Mitts. Use those to burrow into the nearby mound. Emerge on the other side. Note that there's a stool in one of the houses that you can use to heal up.
Head through the tunnel to exit the cave. Follow the path past the Sheikah stone, and drop down on the left to go around the fence that blocked your path. Wait for the Bokoblin to go to the far end of his patrol then run in and jump down left. Burrow down the mound nearby. Go to the left and just go all the way around, destroying the rocks as you go. Shoot the bomb upward to destroy the rock, so you'll be able to reach the second bomb. Tap that to destroy the rocks blocking the exit, go there and return to the surface.
Continue north until you reach a watchtower. Drop down next to it and burrow down the mound next to the fence. Simply head up and emerge on the other side. Pick up your Gust Bellows from the chest. Clear the heated ash in front of you and climb all the way up to the top level. Wait for the Bokoblin to start going away from you, follow it, then go left towards the Mogma house. Wait there until the same Bokoblin goes to the opposide side now (Where you came from), then go left. Carefully avoid the second one as well, following it as it goes away, then using the last fence segment to go around him, and down the mound. Kill the centipede and emerge on the far right. Drop down and pick up the Clawshots.
Grapple your way up north, finishing up with the vines. Go to the left edge and jump down on a drifting platform as it passes by. Ride on it, and jump on the west ledge as soon as you get the chance. Wait for the Bokoblin on the top level to go to the right, then climb up and go left behind the fence. Grapple to the vines on the norhern wall and climb up. Take a bomb flower and roll it into the tower to destroy it, allowing you to pick up your whip from the chest.
Go north across the bridge and pull out the plant using your whip. Clawshot to it and drop down the other side of the gate. Go right, pick up a bomb from near the torch and use it to blow up the stone blocking the cave. Pick up another bomb and roll it into the cave to destroy the other stone. Ride the air jet to the top of the volcano. Go south, away from the Mogma. Once you reach the small village, head left, down the small path. Ride the platform down the lava flow, and jump off on the right, where the bombs are. Pick up a bomb just as one of the platforms is passing, hop onto it and throw the bomb at the tower. Grab your Slingshot from the chest.
Go back up using the hover plants and head west towards the Earth Temple. You can use your Slingshot to stun the Bokoblins here and get to the watch tower, or alternatively you can just make a run for it, briefly luring the first one away from the opening in the fence. The Bokoblins are stupid and easy to outrun. Once you're at the tower, stun the Bokoblin on top with a charged shot of you Slingshot and burrow down the mound next to the watch tower. Go around the left side and roll the bomb to the right to blow up the rocks. Emerge to the surface and pick up your bombs. Dig up the mound next to the chest to make an air jet appear and propel you to the upper level.
Go all the way back up to the volcano summit and use your bombs to blow open the path. Enter the summit and pick up your sword. Go right, wait for the floating platform to arrive, then ride it to the center of the chamber. Go to the door, but jump across to the ledge to your left. Make your way along this path and drop down into a smaller cave. Stick the low hanging water fruit onto your sword and use it to create a crossing on the lava river up ahead.
Jump down, kill the enemies, and pick up the rest of your items from the chest. Climb the south wall twice to reach the top level. Blow up the rock blocking your path and jump back into the starting chamber. Head east again, and ride the floating platform to the central walkway once again. Head through the doorway now and cut the three ropes holding the bridge up (one with the sword, two with the Beetle). Talk to the dragon and receive the first part of the song.