Instructions
Backtrack through the Hyrule Castle Town until you reach the marketplace. This is the area near the center of town where all the stalls and shops are located.
Explore the marketplace until you find a little girl standing by herself. This is Malon, whose father, Talon, owns Lon Lon Ranch. Speak with her once to learn her story. Speak with her again and she will give you a Cucco egg.
Walk back to Zelda's Castle. Approach Talon, the sleeping man. Check your inventory of equipment and the egg should have hatched into a Cucco by now. If it hasn't, walk around a while longer until it hatches.
Equip the Cucco to one of your "C" buttons. Approach Talon and press the "C" button to which you equipped the Cucco. It will call out and wake him up.