After you complete Din's Silent Realm, you receive the Fireshield Earrings, which allow you to reach the Eldin Volcano Summit.
Reach the Summit
From the Volcano Ascent Bird Statue, go east to reach the air geyser. Jump into it, then go southeast into the hot room. Now that you have the Fireshield Earrings, you won't catch fire or take damage in this room. Go northeast up the slope and into the cave.
Extinguish the Flames
Go northeast to the Bird Statue, killing Red Chuchus on the way, then go north past the Bird Statue. More Red Chuchus will attack. Shoot the Cursed Spumes with arrows, then go west over the lava platforms. Go through the cave exit in the west wall.
Skydive off of the northern ledge, aiming for the northwest platform that is visible on the map. Place a beacon there if needed. There is a Goddess Cube on that platform. It unlocks a chest in the thunderhead on the large southwest island. The chest contains a Piece of Heart. From where you activated the Goddess Cube, you can use the Clawshots to get back up. At the top, you can strum the harp near the butterflies to make a Gossip Stone appear.
Drop down into the pond, and while standing in the water, use an empty bottle to scoop some water from here. Then go back into the cave. Go north, kill the big Red Chuchu, and go through the cave entrance there.
Talk to Gorko and, if you did not do so earlier, you will get the ability to dowse for Goddess Cubes. Then pour water into the frog statue to get rid of the flames.
Go back outside to get more water, then come back to the wall of flames. You can strum the harp at the butterflies to reveal a Gossip Stone, who mentions a Piece of Heart nearby. You can't get it yet, so just remember it for later. Use the Clawshots to get up onto the vines on the west wall and walk onto the small ledge above the statue. Pour water into the frog's mouth.
In the next area, Gorko will say that you will need a large container to extinguish the flames here.
Go west from the door and run up to the open window. Use the Clawshots on the vines to reach a platform with a Lizalfos. Kill the Lizalfos and use the Clawshots on the next set of vines to reach a Goddess Cube. It unlocks a chest in the thunderhead on top of the tower of the Isle of Songs. The chest contains a Small Bomb Bag.
Drop down from the Goddess Cube ledge, then go south. In the hot cave, go west to the small pond where you got the water to pour into the frog statues. The Mogma here will tell you that the water source on Eldin Volcano is fed by Lake Floria. Fi tells you to visit the Water Dragon. Fi can add the water basin as a dowsing target.
Get the Dragon's Basin
Go to the green column and descend to the Floria Waterfall statue. While here, use the Clawshots to climb the ivy above the eastern path and reach the Goddess Cube above the door into the cave. It unlocks the chest beneath Fun Fun Island, which contains a Gold Rupee.
From the Floria Waterfall Bird Statue, go into the eastern cave and talk to the Water Dragon. Tell Fi to summon Scrapper to carry the basin.
Return to the sky. You can use the west exit from the Water Dragon's cave to reach the Bird Statue. Fly to the red column of light. You will land at the base of the volcano. You have to protect Scrapper from the enemies as you make your way to the summit. Start by taking the north path. Use the bow and arrows to kill the Bokoblins. (You will find more arrows than usual from enemy drops and from cutting grass and digging in soft soil, so don't be afraid to use plenty of arrows.) There will be more Bokoblins, and Red Chuchus, along the way.
When you reach the Shield Moblin, you can use the beetle to catch a bomb near the entrance to the Thrill Digger game, then drop the bomb on the Moblin to destroy its shield. Then you can use the bow and arrows to kill the Moblin.
When you reach the base of the second steep slope, try to shoot all of the Bokoblins from a distance. There are two hard-to-see Bokoblins on the two wooden platforms near the bottom, and there is another Bokoblin on the stone ledge to the northeast, so try to shoot these before you get too close.
At the temple entrance, use the Bird Statue. It acts as a checkpoint so you don't have to start over from the beginning if Scrapper gets hit. From the temple entrance, look east and try to shoot the Blue Bokoblins from a distance.
To get rid of the Iron Shield Moblin near where the Blue Bokoblins were, you can use the Beetle to pick a Bomb Flower from just south of the temple entrance, and drop it on the Iron Shield Moblin to kill it. Otherwise, you will have to run up its shield to get behind it and kill it.
Cross the bridge where the Iron Shield Moblin was, and keep an eye out for Bokoblins up ahead. Shoot them with arrows, and be sure to look for the one to the east. You can also kill the Iron Shield Moblin with arrows if you have enough and stand far enough back for it to be unable to see you and dodge.
When you reach the hot area, go northeast into the Volcano Summit area. Kill the Fire Keese to the left, as well as the ones in the archway on the right. Go north past the Bird Statue. This statue is a checkpoint, so if Scrapper gets hit, you will start again at this Bird Statue, and any enemies you killed will stay dead.
Before you go down to where the Lizalfos are, be sure to get rid of any nearby Fire Keese, and use arrows to shoot the Cursed Spumes in the lava to the northwest of the Bird Statue.
Then jump down to the Lizalfos and keep an eye on both of them to make sure neither one is attacking Scrapper.
When they are gone, jump over the lava platforms and turn right. There are no more enemies along the path, so just go north and keep going north to reach the wall of flame at the temple. Scrapper will automatically pour the water in. Go inside to enter the Fire Sanctuary.