1º Complete Irma's side quest in Sirion (after you can move freely around Hyrule). If you're already in the last moments of the game, enter the snowpeak at the east exit of Sirion. At the end you will find a cave where you will find the ring.
2º Obtain the Champions Cup in Sirion (it's the last cup).
3º Complete the Skull Kid mission (Majora's Mask).