After completing the Temple of Droplets, you should infuse your sword, then look for the ghost.
You'll see a ghost who marks your map with your next destination. You'll also be reminded that you need to go back to the elemental sanctuary and power up your sword.
Before all that, there are two Kinstone fusions to be had, both in the Minish Woods. Use the ocarina to get there.
First, fuse with the Minish in the little house west of the Minish village. Then, fuse with the Minish elder in the village. Go back to the first Minish you visited to get the remote bomb. If you want to use normal bombs again later, just go back to this Minish to trade. You can only set one remote bomb at a time, but you can set it off whenever you want with the bomb button. The chest that appeared in the Wind Ruins is a bigger bomb bag, get it if you want.
Now use the ocarina to get to Hyrule Town.
At the Inn, you can light the two torches in the top floor room at the bottom to open the door, giving access to the roof with a red Kinstone piece in a chest.
The school is now open, and there's a Minish path in the playground that should have a chest in it from an earlier fusion. To get there, use the Cane of Pacci to flip over the big pot and make it a shrinking portal. Take the bottom right blue arch to get out to the playground, and go east to find the path. The chest contains a red Kinstone piece, and above that is a rock that you won't be able to push out of the way until much later in the game, so leave.
Still tiny, go back into the schoolhouse, and find the blue arch at the bottom left. Outside, climb the ladder, talk to the Minish if you want, and grow and grab the chest (red Kinstone piece).
While in here, you can push aside the statue of Minister Potho to reveal stairs leading down. There's actually a better path to this area that puts you in a position to get two treasures instead of one. You can't access it just yet but you should wait until you can, otherwise you'll be wasting some bombs.
When you're ready head north to North Hyrule Field, and from there north to Hyrule Castle Garden.
Hyrule Castle Garden
Guards are blocking the main entrance in, so you have to find another way in. But first there are a few things to do.
First head east. If you were here earlier you've already cut the bushes and there's a ladder going down. If not, cut the bushes and go down. Grab the piece of heart, then light the torches in the corner and talk to Grimblade to learn the sword beam skill.
Back outside, there's a tree to dash into to create a shrinking portal if you didn't already, and a Minish house in the northeast corner.
There's also a drained fountain to go down with a piece of heart there if you didn't get it before.
Next go to the west side of the garden. You need to sneak past all the guards in the hedges here. First stay just above the path leading in so the soldier can't see you when he comes down to the entrance to the maze. Then when he goes back up, rush in when he's at a safe distance and get to the right side of the small piece of hedge. Wait for him to go back down, then continue north and get to the corner below where the next soldier is walking. When he walks toward the right, rush up and left and down out of that section of hedge. The next part is tricky, the way I did it was to wait until the third guard walks all the way right, and at that time the fourth guard was walking down so I had a clear shot to walk around behind the fourth guard and north to the destination area.
Before moving on, go down the stairs where the fountain was drained to reach a fountain with a few fairies floating around. Next go back out, and cut down the bushes to reveal a ladder. Go down.
Hyrule CastleFollow the path, beating the ropes along the way, and step on the switch to open the door. Go through. The door to the courtyard to the sanctuary is straight north.
Elemental SanctuaryPress R at the pedestal to infuse your sword with the water element. Now you can split into three instead of two. To get back out, split below to step on the two switches. Follow the path you took into the castle, and once in the garden talk to a guard to get kicked out of that area of the garden. Exit south to go back to North Hyrule Field.
North Hyrule FieldHead west. Before heading down the ladder, get in the water and swim around the rocks to go north one screen. There is a chest here at Hyrule Castle Garden containing 200 rupees. Back in the last screen you can swim west and north to another area of Hyrule Castle Garden for another chest, this one containing 100 mysterious shells.
Back out of the water, go into the door or down the ladder. There are glowing tiles here and a large block that needs to be pushed by three copies of Link, so do it. Climb up the ladder on the other side. Head north up the stairs and there should be a chest here containing 200 mysterious shells. Exit west.
Royal ValleyIn this creepy place you'll want your lantern on at all times. Down the stairs, be careful of the ghost. If it gets too near, it grabs you and hurts you until you tap the buttons to escape. Once the ghost is out of the way, notice two pieces of fence by the wall. Put a bomb there to open a cave. Inside is a great fairy fountain. She will ask you questions about your adventure. The correct answers are, in this order: no, no, yes, no, no. If you get any question wrong, she takes away all your arrows. But luckily, even if she takes them all away you can keep trying, and once you get it right, she gives you a large quiver and gives you back all your arrows.
Once you're done in there, continue on and head north, being careful of the ghosts and crows that attack.
You enter the Lost Woods, where you have to follow a specific path to get out. There is a ghost in each screen, and it's dark where the lantern doesn't shine, so be careful. The signposts will tell you which way to go, but some of them won't tell you directly, instead they tell you to go the same direction as you went a few screens ago, for example. The correct path to get out is up, left, left, up, right, up.
Once you're out, head northeast to Dampé's house. He'll give you the graveyard key, but back outside a crow will steal it. Equip the pegasus boots on the sword button (so you can keep the lantern on) and find the tree where the key is. Don't get too close to the tree or the crow will fly it to another tree. Dash into the tree and grab the key. BE SURE to re-equip your sword if you unequipped it.
Go back to the graveyard gate and talk to Dampé to have him open it for you. In the graveyard, go straight up and push the tombstone up to get it out of the way. Then go left and up to where a lone tombstone stands, and push it up to reveal steps. Down below, split into three to push the block out of the way and reach a piece of heart.
Back outside, go towards the gate then right and find some rocks on the ground. Break them to reveal glowing tiles. Split into three, then walk left through the path past the first tombstone you pushed up, then go up past the flowers and right to the switches. Step on them to move the big tombstone. Go down the steps to reach the Royal Crypt.