In The Legend of Zelda: Twilight Princess, Link and Midna take on the task of collecting the three missing Mirror Shards that had broken off from the Mirror of Twilight. Their goal is to go to the Twilight Realm and defeat Zant, but the Mirror of Twilight is their only link to that world. They take on this quest after going to the Mirror of Twilight on top of Arbiter's Grounds and discovering it has been scattered into four pieces. The first Mirror Shard remains within the Mirror while the rest are hidden all around Hyrule.
The Second Mirror Shard
The second Mirror Shard is found in the north-east of Hyrule on Wii and the North-west on GCN. It is located at the top of Snowpeak mountain. When Link and Midna go there, they see a large mansion. Upon enetering, they discover that the inhabitants of the mansion, Yeto and Yeta, have hidden the Mirror Shard away in their Bedroom because it was making Yeta sick. She then shows Link where she hid the Bedroom Key on his map. He goes off to find the key. When he gets to the right location, he opens the chest to find an Ordon Pumpkin. Link then heads back and Yeta shows him another location. This time, he opens up the chest to find Ordon Goat Cheese. Now Midna is really getting angry. Link heads back to Yeta and she tells him of one more location. This time, it is the right location. As Link walks up to the Bedroom with his Bedroom Key he meets up with Yeta, who says she will accompany him. Once they enter the room, Yeta shows Link the Mirror Shard. The Mirror Shard seems to possess her, and turns her into the dungeon boss, Blizzeta. Once Link defeats her, he takes the Mirror Shard, returning Yeta to her original form.
The Third Mirror Shard
The third Mirror Shard is obtained in the Temple of Time. Link visits the Sacred Grove in hopes of finding the next shard. When Link places the Master Sword back into the Temple of Time, a statue in front of a gate near the entrance to the Master Sword chamber will disappear. Link discovers that this is actually the Door of Time, and it transports him back in time to when the full Temple of Time still stood. Once again Link must place the Master Sword into the pedestal, and this time stairs appear, leading to the dungeon. Ooccoo and her son run up the stairs ahead of him, and later meet with him in the temple, explaining that they are searching for a way to get back home.
The Final Mirror Shard
The fourth Mirror Shard is found in the City in the Sky. It turns out that Ooccoo was searching for the Dominion Rod to get back home. After Link restores its drained power via Owl Statues across the land, he can use a cannon repaired by Fyer to reach the City in the Sky, which is home of the Oocca, Ooccoo's race. Link enters the dungeon here and finds a second Clawshot. He can use that to defeat the boss, Argorok, who was also guarding a the final Mirror Shard.
The three shards can then be taken back to Arbiter's Grounds and used to form the full Mirror of Twilight.