After you complete your first train ride, you arrive in Hyrule Castle Town.
There isn't much to do in Hyrule Castle town just yet. Someone on the train platform will ask you a question. Answer however you want.
There is a sign near the entrance that can teach you about Prizes and Battles. The idea of prizes is to buy a bunch of prize postcards from a shop, then put them in the mailbox. The more you mail, the more likely you are to get a good prize. There is a first prize, a second prize, and a third prize each day.
You might notice treasure chests on the rooftops. You can't reach those yet.
There is a shop near the north exit, although you might not be able to afford anything there yet.
If you go to the mailbox in the back of town, you'll notice that it's bouncing. Tap on it and the postman will appear and give you a letter. To read it, tap the Menu button and then tap Collection. Tap the letter on the right side of the screen, and tap the unread message. It's just a letter from the Postmaster.
If you're done exploring the town, you can go north to the castle.
There isn't really anything interesting around the castle grounds right now, so just walk up to the guards at the gate. Talk to the guy on the left and say that you're here for the graduation ceremony. Then go inside.
Talk to the guard straight ahead. He'll tell you to leave, but then Chancellor Cole will walk up. He wears two hats and he's really mean. He seems totally suspicious. Follow the Chancellor up the stairs.
The ceremony will take place. The Chancellor is extremely rude during the whole thing. Zelda secretly hands Link a note.
After the ceremony is over, tap Menu, Collection, and the letter tab, and read the note from Zelda. Do what the letter says and tap the map button that is just below the letter on the left side. Then copy the path from the top map onto your map on the bottom (just draw it by hand.)
To get to the secret path, exit this room through the south exit. Then head to the southeast corner of the room and head up the stairs. Now you're in the place that was marked with the arrow on Zelda's map. Follow the arrow. There is a ledge along the side of the castle that you can cross to get to the door marked with the X. When you get to that door, hop down and go into the door. Inside, go up the stairs in the upper-left corner of this area.
You've reached Zelda's room. Tell her that you can take her to the Tower of Spirits on your train. Follow Zelda out of the room. Now you will have to escape the castle secretly.