Instructions
Travel to the Lon Lon Ranch as Young Link in the first portion of the game.
Equip your Fairy Ocarina to an available item slot and talk to Malon, the little girl who is singing in the middle of the ranch.
Press the item button that you assigned your Fairy Ocarina to when Malon asks you about music. You will show the Fairy Ocarina to Malon who will teach you a song.
Press the buttons "Up-C," "Left-C" and "Right-C" on the screen as instructed to by Malon to learn how to play Epona's Song on your Fairy Ocarina.
Return to the Lon Lon Ranch after you travel through time and start playing as Adult Link. You must travel to the Lon Lon Ranch during the day, so either use the Sun's Song on your Fairy Ocarina to change the time of day or wait a few minutes for the sun to rise.
Talk to Ingo in the middle of the ranch. Agree to pay him ten rupees in exchange for getting to ride one of his horses. A horse will approach and the timer will start.
Play Epona's Song on your Fairy Ocarina instead of mounting the horse that Ingo has selected for you. This will summon the horse Epona. Press the "A" button to mount Epona.
Target Ingo while riding Epona by pressing the "Z" or "L" button to speak with him. Accept his challenge to a race for a bet of 50 Rupees.
Race Ingo twice while riding Epona. After you beat him for the first time he will challenge you to a rematch with Epona as the prize. To beat Ingo, stay close to the wall and give Epona a boost of speed using a carrot by pressing the "A" button.
Jump over the far wall of the ranch when Ingo tries to trap you after the second race. Build up speed by using carrots and approach the wall at a straight angle to make the jump.
Play Epona's Song while out in the field to summon your new horse whenever you want to ride it.