Throughout The Legend of Zelda: Oracle of Seasons, Link will acquire many different items. By successfully trading them, he will eventually acquire the Noble Sword. The Noble Sword can actually be obtained without going through the trading sequence by following the correct path in the Lost Woods, but the Trading Sequence is required in order to be able to buy Magic Potion from Syrup.
The Cuccodex can then be taken to Malon, who is having a difficult time taking care of her Cuccos. She is grateful and gives Link a Lon Lon Egg. This can be done immediately after receiving the Cuccodex.
In Mrs. Ruul's Villa, Link finds Mrs. Ruul herself, who is being afflicted by the summer heat. Upon showing her the Ghastly Doll, she gets shivers down her spine and asks for it. In return, she gives Link an old Iron Pot. This trade can be done any time after the completion of Poison Moth's Lair.
The Iron Pot can be taken to the Subrosian Chef, who resides in northwestern Subrosia. He prepares Lava Soup, puts it in the Iron Pot, and gives it back to Link. This trade can be done immediately after receiving the Iron Pot.
The Lava Soup is then taken to Biggoron, who has been suffering from a cold. The Soup clears his cold up and Link is given the Goron Vase in thanks. This trade can be done immediately after receiving the Lava Soup.
The Goron Vase can then be taken to Ingo, an avid vase collector. In exchange for the final vase of his collection, he gives up his Fish. This trade can be done any time after the completion of Dancing Dragon Dungeon.
Just north of Horon Village and west of Eyeglass Lake is a man who is trying to get his cat, Mittens, down from a tree. After giving him the Fish, the cat immediately comes out of the tree. Since he no longer needs his Megaphone he used to try and call Mittens back down, he gives it to Link in exchange. This trade can be done any time after receiving the Fish.
In a cave on Mt. Cucco, Talon can be found sleeping next to a large sack. If Link wakes him up with the Megaphone, he will give Link the Mushroom. This trade can be done any time after receiving the Megaphone.
The Mushroom can be given to Syrup who lives in a small shop in the middle of the Sunken City. To reach her shop, change the season to winter on the stump north of the shop and climb up the embankment. Syrup will give Link the Wooden Bird in exchange for the Mushroom. She will also sell Potions for 300 Rupees each from that point on.
The Wooden Bird can be given to Tick Tock, who has been looking for the perfect bird for his cuckoo clock. He will give Link Engine Grease. This trade can be done any time after receiving the Wooden Bird.
The Phonograph can then be taken to the music-loving Deku Scrub. The Phonograph is not actually traded away, as the Deku Scrub only wants to hear its music; the item is retained in Link's inventory for the remainder of the game. In exchange for the music, it tells Link how to find the Noble Sword. Head north and then west and hop on the stump. Change the season to winter and head west. Hop on the stump there, change the season to autumn and head west. Hop on the stump, change the season to spring, and head west again. Hop on the stump one final time, change the season to Summer, and head west. There in the pedestal will be the Noble Sword, or the Master Sword if Link has already obtained the Noble Sword from a Linked Game Secret.