Instructions
Travel to Kakariko Village as an adult. Talk to Anju, the Cucco Lady, and she will give you a cucco egg to take care of.
Keep the egg in your inventory for about two days. You can play the "Suns Song" on the ocarina to speed to the next day. A message will pop up informing you that the egg has hatched.
Take the hatched cucco to Talon, who is sleeping in the house in the center of town. Wake Talon with the cucco by taking it out of your inventory while in front of him. This will make the bird very happy.
Take the cucco back to Anju, who will remark about its happiness, and give you Cojiro as a reward.