Eastern Hills and Hyrule Town
After the discussion between Princess Zelda and your grandfather, go down the stairs and go right to join them. Your grandfather asks you to head for the castle and entrusts you the Smith's Sword! Follow Zelda outside, go to her and follow her until you reach the party. Upon arriving, talk to the inhabitants to learn more or less important information, then talk to Zelda several times. She then wins a Small Shield and gives it to you. Go north towards the castle. Follow the princess, stand in front of the Deku Scrub and raise your shield. Go on to the north and get into the huge building.
Hyrule Castle
Talk to Minister Potho on the steps. The ceremony will begin and Sir Vaati, the champion, arrives. He opens the chest from which evil spirits are fleeing away and shatters the Picori Sword. Zelda then uses her Light Power to try to stop him. Link is not able to protect his friend, who gets turned into stone by Vaati.
In the bedroom, press A to get up. Talk to the maid, then go left. The Hyrule King will tell you about the Minish dwelling in the Minish Woods. Link is chosen to meet the Minish who will be able to forge a new sacred sword. The King will entrust you the Broken Picori Sword as well as the Smith's Sword. Your grandfather will also give you the Hyrule Map to help you find the Deepwood Shrine. Leave the castle by keeping going south and go through the garden.