With the hammer, you now have access to much more of the Dark World than before. Let us explore this evil place and win items to help us save the maidens and destroy Ganon!
If you exit the area of the Palace of Darkness through the southwest mountain pass, then exit west, you find a bridge leading south, blocked by nine posts. You can hammer those posts into the ground and move past them, so do it! From here, you can reach much of the rest of the Dark World.
Head west to where your house is in the Light World. This is the bomb shop, where a strange creature dressed like you sells bombs! You will need to come back here later, but there's nothing to do here for now. Head west, then south, then west again.
There are trees with eyes here. If you touch their mouths, you will bounce off and they will spit a bomb. Be careful not to let it explode on you. You can then talk to the tree, who will either yell at you for bothering it, or will give you some advice.
You will see an arrow of purple bushes pointing down. Follow them down to an area behind a big rock where a green and orange monster is bouncing. Kill the monster, then cut one of the purple bushes and go inside the circle. Use your Magic Mirror to go to the Light World. Go into the cave here, lift the pots, and collect the heart container!
Go back outside and back into the warp to the Dark World. Go north, cutting through the arrow of purple bushes, into the clearing. A creature is standing on a tree stump here; talk to it. He is the boy who used to play the flute in this clearing in the Light World. He buried his flute with some flower seeds (in the Light World). Tell him you will try to find it, and he gives you a shovel. Go to the upper-left corner of the clearing where there are some flowers (don't stand on the flowers), and use your Magic Mirror to go back to the Light World. Dig around the flowers here to find the flute! If you stand around long enough you'll see the boy play his flute and disappear. (There must be some weird time-travel stuff going on.)
Go back to the Dark World and talk to the creature, who laments that he is no longer able to play his flute, so allows you to take it, telling you to give it to an old man in the inn in the Light World. The creature then asks you to play the flute for him one last time, so use Y to play it. The creature turns into a tree..?
Anyway, go to where Kakariko is in the Light World. There is an archery game if you want to try to win some rupees, and there is a digging game further west. Talk to the old man to play the digging game for 80 rupees (he gives you a shovel). There is a piece of heart hidden near the center of the field, so dig around there to find it. If you don't find it, leave the screen and go back for another chance. Keep trying until you find it.
In the Dark World, you can't go any further into the Kakariko area from the archery game, because of the large black stone that you can't lift. Use your Magic Mirror to go to the Light World, and go into Kakariko. If you go to the inn, you can play the flute for the nodding man, who tells you to play it for the bird in the village square. Go to the weather vane in the center of town and play the flute in front of it. It bursts open, revealing a bird! Now, whenever you play the flute, the bird will fly into the screen and pick you up. You will then see the world map with various areas numbered. You can highlight any number and press A, and the bird will fly you to that spot. Now it is much easier to travel around Hyrule!
Use the flute now, and choose number 1, on Death Mountain. Climb to the top of the mountain, avoiding the deadrocks and fighting the tektites, and approach the Tower of Hera. Take the wooden bridge to the west of it. You reach a monolith with an ancient Hylian inscription. Use the Book of Mudora, and it will tell you to hold up the Master Sword, which you do automatically. The Ether medallion falls from above, and the monolith crumbles. Using this medallion uses lots of magic to create a sort of shockwave, killing all enemies on the screen.
Play the flute, and choose 4, your house. From here, go north and through the castle gate to get back to the Dark World. Use the hammer to get to where your house is in the Light World, and go south into the swamp, then west into the desert. Go as far west as you can go, beyond some purple posts. Use the Magic Mirror beyond here, and you end up on a mountaintop. Go west to the next screen, and you find another monolith inscribed with ancient Hylian. Use the Book of Mudora, and the Bombos medallion falls from above (killing the circling vulture). It uses a lot of magic to create explosions around the screen, killing all enemies.
Go back to the warp point you left to the east, and step into it, then go east to the swamp. You find the Swamp Palace here, but if you go inside, you can't go any further than the entryway. If you touch the tile on the wall, Sahasrahla tells you that if you change something in the Light World, it will change in the Dark World, and vice versa. Remember the building in the Light World swamp with the floodgates? Use the Magic Mirror outside, and go into the building, and pull the right-hand lever to open the floodgates. Then step into your Dark World warp to return to the Swamp Palace. Go inside, and the duct is filled with water!