After you find your sword, the owl tells you to go to the Mysterious Forest. There, the owl says to look for a key.
Find the Toadstool
The owl will tell you that there is a key hidden in this forest that you can use to open Tale Cave to the east.
Go east until you find a hollow log. Go into it.
Don't stand for a long time on the cracked floors around the edge. If you do, the floor will break and you will fall into the hole.
Go around and break the crystals with your sword. There is a rock in front of the treasure chest. Push it to the side after you have broken the crystals, then open the chest to get 50 rupees.
Go north, but be careful of the green Zols that are hiding in the floor.
Go to the next room. Push the rightmost rock down, then push the one next to it down. Unfortunately you can't get the Piece of Heart yet, so just go south to leave the room.
Outside, you find a toadstool. Walk over to it to pick it up.
Get Magic Powder
There is a dead end to the north, so go back through the cave.
To go through the rock puzzle, here is a diagram where each rock has a number:
01 02 03 0405 06 07 08 0910 11 12 1314 15 16
Push rock 11 to the right, then push rock 04 up, then push rock 07 to the right, then push rock 05 up. Then you can exit to the right. Keep going and exit the cave.
From the screen with the hollow log, go north until you reach a screen with a hollow log that is blocked by rocks. Go east from there and you see a Piece of Heart that you can't reach. Go south from there and follow the path until you see a tree with a door in it. Go inside.
Press Start and equip the toadstool, then use it on the witch. She gives you Magic Powder. You can use it on the torch in this room to light a fire.
Use the Powder on the Raccoon
Now go back to the forest. Go west from the hollow log that you went into before, then go north. Use the Magic Powder on the raccoon. The raccoon turns into Tarin.
Go north from this screen to find a treasure chest. Open it to get the Tail Key.
Go to Tail Cave
To reach Tail Cave, go to the beach. Tail Cave is one screen north of Sale's House o' Bananas, which is north of where you found your sword.
To open the dungeon, walk up to the keyhole. When you're ready, go into Tail Cave.