There are only four Special items in the game, but they serve very important purposes.
These boots let Young jump by pressing X on the keyboard. This allows him to jump over holes and other obstacles in his path.
Talk to Orange Fish. Obtain the cardboard box from him, then take it to the merchant by going down twice. Trade with the merchant to gain biking shoes, which should be taken to Mitra by going left twice. Mitra will give you the Jump Boots.
Should you fail to acquire the boots before reaching the cliffs area, Mitra will automatically give you the boots. The trading sequence will then result in a health refill instead.
Unlike the Jump boots, the keys are fairly easy to acquire. The keys open special gates throughout the land of Anodyne.
Simply defeat the boss of the Temple.
Simply defeat the boss of the red sea dungeon.
Simply defeat the boss of the cliffs dungeon.