After obtaining two of the elements, you should return to Hyrule Castle to infuse the Picori Blade.
Get the Repaired Sword
After you have completed the Cave of Flames dungeon, if you haven't talked to Melari again yet (i.e. if your sword is still Smith's Sword), shrink down and enter Melari's Mines. If you haven't completed the first 22 Kinstone fusions in the game, some of the Minish in the Mines may have Kinstone fusions for you.
Talk to Melari to obtain the White Sword. Your goal now is to find the Elemental Sanctuary in Hyrule Castle.
Use the west exit of Melari's Mines. To leave the mountain, use the shrinking portal to grow to normal size, then go south from the shrinking portal and fall down from the ledge. Go down the ladder. If you have already talked to the Crenel Hermit, or if you don't feel like visiting him, go east until you can't go farther east, then climb down the climbing wall and keep going south to reach Mt. Crenel's Base, and skip the rest of this paragraph. If you want to visit the Crenel Hermit, you can go down the ladder south of there, then go west and climb up the climbing wall. When you reach the top, go west and go down the ladder there, then enter the cave. Talk to the Crenel Hermit, and if he has a Kinstone fusion, you can fuse Kinstones with him as well. Then go outside, up the ladder, down the climbing wall, then at the bottom, go east, and down the ladder, ignore the vine and keep going east, and when you can't go farther east, climb down the climbing wall at the end to reach Mt. Crenel's Base.
Go to the east side of Mt. Crenel's Base, and go south from there, then go east to reach Trilby Highlands. Keep going east, and follow the dirt road to reach Hyrule Town.
Hyrule Town
Swiftblade can now teach you a new technique. His cabin is southwest of Mama's Café.
Buy the boomerang in the shop if you haven't already.
You can use the Cane of Pacci on giant pots to flip them over and turn them into shrinking portals. There is one in Mama's Café, as well as in Romio's house (one of the houses east of the shop). While you are small, you can go through small archways in houses, and you can enter fireplaces if there isn't a fire there. You can also talk to animals, and they may have Kinstone fusions, but cats will try to attack you.
Shrink in Romio's house and go through the small archway in the southwest corner of the house, then go northeast to find a vine next to the inn. Go up the vine, then go around the back of the inn to find a path marked with flowers. Walk between the flowers to find a room with a shrinking portal and a Piece of Heart. Use the portal to grow, take the Piece of Heart, then shrink again and make your way back to Romio's house to grow again.
Also while small, you can go into the back of Wheaton and Pita's bakery, and if you climb up and past the puffs of steam to reach a hole. Go in and you can find a chest in the rafters area that contains 100 rupees.
Go back to Romio's house to grow to normal size, then go into Mama's Café and use the Cane of Pacci to flip over the shrinking portal if you haven't already, then shrink to Minish size. Go through the southwest archway in the café to go outside, then go west to find a stone ramp with a wooden plank on it. Go across the wooden plank, then go north and talk to the dog that is blocking the stairway. This will make the dog move out of the way, which will allow you to access this area at normal size.
To return to normal size, go between the flowers at the north edge of the cabin in this area, and use the shrinking portal.
South of the cabin, you find Carlov's hut, where you can trade Mysterious Shells for a chance to win figurines. See the Carlov's Figurines page for more details.
North Hyrule Field
When you're ready, go north from Hyrule Town to reach North Hyrule Field. Go to the northwest part of the area and bomb the rock, then climb down the ladder. Go down the stairs to find a Piece of Heart. Leave and continue on to Hyrule Castle.
Hyrule Castle
In the castle, go northwest up the stairs, then go down the stairs north of that. Follow the path and go through the door in the wall to the north. Then keep going north to find a glowing door. Go through to enter the Elemental Sanctuary. Keep going north and the door will close behind you. Go north onto the platform and go around to the north edge of the small platform in the middle. Press A or R to drop your sword into the slot in the platform. Your sword will be infused with the two Elements that you obtained. There will be a cutscene explaining your new power.
Stand on one of the two glowing tiles near the stone tablet, then hold the sword button to charge up your sword. When the gauge is full, keep holding the sword button and walk onto the other glowing tile. You will split in two. Whenever you use this power, your copy will move around as you do, but will always remain the same distance apart from you. If it hits a wall or barrier or enemy, it will disappear. It will also disappear when the power gauge becomes empty.
Go south to the four glowing tiles near the entrance. Stand on one of the two middle tiles, charge up your sword, and keep holding the sword button and step on the other middle tile. Then walk south onto the two switches to activate both at the same time. The door will open. Go through.
Now you can leave the castle and begin your search for the next element.