After you get the Pendant from the Desert Palace, you can collect a number of treasures before you proceed to the third palace.
Get a Piece of Heart
From the Desert Palace, go east and fall off of the ledge. Then go southeast to find a cave entrance. Go inside. Follow the path through the cave until you find an old man. Use a bomb in the middle of the south wall to open it (a dash attack is not strong enough to open it). Go through and open the chest to get a Piece of Heart. Then go back outside.
Get Rupees
Go south as far as you can go, then go east to exit the desert. Go to the two large white stones in the middle of the area and pick up the southernmost one. Go down the stairs there. Pick up the pots to get rupees. You can then exit and reenter this cave and pick up the pots to find more rupees. You will need at least 500 rupees to collect some of the items listed on this page, so you can keep going into and out of this cave until you have that much. If you feel like it, you can keep doing this until your wallet is full.
Get the Magic Powder
Outside of the cave, go east. Whenever you see a rock that starts walking around, you can lift the rock to reveal a Hoarder, which will spit out rupees for a few moments before it disappears. The faster you gather these rupees, the more rupees it will spit out before it disappears. If you bump into it, you will be knocked back (but not injured), and this can make it difficult to gather the rupees quickly, so try to clear the area around the Hoarder before you lift its rock.
Go east to exit the desert, then go north in the swamp, then east, then north to Link's house. Go east from there, then go east so you can cross the bridge, and go north to the next area. Keep going north, and ignore the bridge on the left as you continue north. Then go east and you will find the Witch's Hut.
The Buzz Blob will zap you if you hit it with your sword. If you hit it with your Boomerang to stun it, you can safely hit it with your sword while it is stunned.
Equip the Magic Mushroom (if you don't have it, see "Gather Items in the Lost Woods" for directions to it) and use the mushroom on the witch, who will take it and tell you to come back later.
Go west to the next screen, then go east to return to the screen with the Witch's Hut. Go into the hut, then walk up to the bag next to the potion salesman and press A to take it. This is the Magic Powder, which you can sprinkle on enemies to transform them. For example, sprinkle them on Bubbles (the floating skulls surrounded by four orbs) to turn them into Fairies. You can also sprinkle it on Buzz Blobs to turn them into Cukemen, whom you can talk to, but they don't have much to say. Cukemen will still zap you if you hit them with your sword.
Get the Flippers
Go back outside, and go east from the Witch's Hut. Pick up the large white boulder, then throw it, then go northeast to the next area.
Follow the path and you will reach some piles of rocks. Hold the A button to dash into the piles to destroy them. Then you can go east and north to the next area.
Go northwest and jump down the ledge to reach the grass next to the water. If you get hit by a Sand Crab, you lose two hearts, so be careful to avoid it. Go north along the grass, and continue going north along the shallow water to reach the next area.
This is Zora's Domain, and Zoras will appear from whirlpools in the water and spit orbs at you, or will jump up from shallow water and start walking toward you. Walking Zoras will be stunned if you hit them with your sword, and you can pick them up and throw them back into deep water (or just keep hitting them to defeat them).
Go north along the shallow water, then northeast when the path splits. Continue following the path. When the path splits again, go south along the shallow water until you can go no farther south, then go east and follow the path until you reach a large waterfall. King Zora will pop out of the water. Buy the Flippers from him for 500 rupees. If you don't have enough, be sure to come back here and get them.
The flippers give you access to teleporting whirlpools throughout Hyrule. Swim into one of these whirlpools and you will be teleported to another part of Hyrule.
Get a Second Piece of Heart
After you get the Flippers, go south and swim down the waterfall there. Then walk along the shallow water, which will take you to a grassy area. Go to the end of the grassy area to find a Piece of Heart.
Get Upgrades at the Waterfall of Wishing
Go east from where you got the Piece of Heart, and swim south down one of the waterfalls. From there, go west, then south to exit Zora's Domain.
Go west, then northwest to the waterfall. You can swim north through the middle of the waterfall to enter a hidden cave. Go north and you will find the Mysterious Pond. You are asked to throw something in. Throw in your Boomerang. When the Fairy asks if you threw the Boomerang, say yes, and you will receive the upgraded Magical Boomerang. It flies farther and faster than the original.
Approach the Mysterious Pond again, and this time, throw in your Shield. You will receive the Red Shield, which can block orbs like the ones that the Zoras spit out. It blocks orbs even if you are swimming. It can't block Beamos beams, however.
If you have any empty bottles, you can optionally throw one into the pond and it will be filled with Green Potion, which refills your magic gauge.
Upgrade your Bomb and Arrow Capacity
Leave the cave of the Mysterious Pond, then swim south and you will see a whirlpool. Swim into the whirlpool to be teleported to Lake Hylia.
Swim north onto the small dock, then go north into the cave. This is the Pond of Happiness. You can throw rupees in, and after you throw 100 rupees, a Fairy will appear and ask if you want to upgrade your bomb capacity or your arrow capacity. After your first upgrade, you will be allowed to throw more rupees at a time. The maximum number of bombs that you can carry is 50, and the maximum number of arrows that you can carry is 70. If you are already at your limit, the Fairy will return your rupees. It costs a total of 1400 rupees to fully upgrade your bow and arrow capacity. You can get infinite rupees from the underground room hidden under a white boulder just east of the desert in southwest Hyrule.
You can bomb the cracked wall to the east of the Pond of Happiness to find a room with some small Fairies.
Get a Magic Bottle
Go outside and swim north from the island along the narrow waterway that goes northeast. Continue swimming along the waterway and you will find a bridge. Swim under the bridge and talk to the man there to get a Magic Bottle.
Get the Ice Rod
Go back the way you came to reach Lake Hylia. Swim to the southeast of the lake and go east there to reach the next screen. Go east to find a dock. Swim onto it to exit the water, then go north to the next area. Go to the east wall, then go north. To the west, you will find a cave entrance. You can lift the large boulder to find a cave where you can lift the pots to get 20 rupees. Back outside, bomb the boulder in the north wall to open a cave. Go through. Go north in the icy cave and open the chest to get the Ice Rod. This is the treasure that Sahasrahla mentioned earlier.
Get the Good Bee
Go back outside, and go into the cave entrance on the right. Go north and bomb the north wall, and go through. Hold A to hit the statue with a dash attack, and a bee will come out. This is the Good Bee, which you can catch with the Bug-Catching Net if you have an empty bottle. If you let the Good Bee out of the bottle, it will kill all of the enemies on the screen. Once all of the enemies are gone, the bee will fly back to you, and you can catch it again with the Bug-Catching Net. If you lose the Good Bee, you can dash into the statue in this cave again to get another.
Get a Third Piece of Heart
Go back outside, then go south and jump into the water. Swim southwest to reach the next area, then swim south down the waterfall. Swim into the whirlpool to the south, and you will be warped to a small pond near the Sanctuary. Swim north onto the dock to get out of the pond, then go east and you will find a couple of trees near a cliff. Go east while staying near the cliff. In the next area, dash into the pile of rocks to reveal some stairs. Go down the stairs and open the chest to find a Piece of Heart.
Continue On
Now that you have gathered all of the new treasure that you can reach, your next destination is up the mountain.