Young Link's Mask Trading Sequence
Right after you get a letter from Zelda, talk to the guard blocking the entrance to Death Mountain. He will tell you that the Happy Mask Shop just opened, and ask you to get a mask for him. This is where the mask trading sequence starts.
Keaton Mask - Give the Keaton Mask to the guard in front of the entrance to Death Mountain, and he will pay you fifteen rupees for your troubles.
Skull Mask - Give the Skull Mask to the Skull Kid in the Lost Woods.
Spooky Mask - The kid in the Graveyard would like to look spookier than he does, so he'll gladly take this mask off your hands.
Bunny Hood - The Running Man running throughout Hyrule Field wanted to look like a bunny, and will give you more money than you can count, but he will only appear after you beat Barinade inside Jabu-Jabu.
After you sell the Bunny Hood, the Goron Mask, Zora Mask, Gerudo Mask, as well as the Mask of Truth will become available to you. Talk to different people with them on to get different responses. If you wear the Mask of Truth in front of a Gossip Stone and press A, you will be told strange things that don't really have anything to do with anything.

Adult Link's Trading Sequence
Pocket Egg - Adult Link's trading sequence starts in Kakariko Village. Talk to the cucco girl, and she will give you a pocket egg. When it hatches, use it in one of the houses, in front of Talon. You'll find him sleeping in a bed. After you wake him up, go talk to the cucco girl again.
Cojiro - Go to the Lost Woods with your new cucco. Give it to the cucco girl's brother. He can be found near the entrance to the Lost Woods where the Skull Kid used to be. Pull out Cojiro in front of him, and he will give you a mushroom.
Odd Mushroom - Go back to Kakariko Vilage. Go to the potion shop at the far left end. Inside is a witch who will give Link a potion.
Odd Potion - Now that you have the potion, return to where the cucco girl's brother was (Lost Woods). Instead, there will be a Kokiri girl there who will give you a saw in exchange for the potion.
Poacher's Saw - Go to Gerudo Valley, and talk to the carpenter outside the tent. He will give you the Goron's Sword in exchange for the saw.
Goron's Sword - Although this broken sword looks worthless, it's really not. Take it to Biggoron on the very top of Death Mountain, and he will agree to repair it if you get him some eye drops.
Prescription - Take the prescription to King Zora in Zora's Domain. He will give you an eyeball frog, which you need to make the eyedrops.
Eyeball Frog - Take the eyeball frog to the professer in the house at Lake Hylia. He will make you some eyedrops with it.
Eye Drops - Quickly take the eye drops back to Biggoron. He will put them in his eyes, and give you a claim check. Come back in three days, and the sword will be ready. The quick way to do this is just to play the Sun's Song six times, and the sword will be ready. Now you have the most powerful sword in the game. The only downside is that it's so big that you can't have your shield out at the same time.