How do you find princess zelda?

Princess Zelda is in Hyrule Castle, which you can only access during the day.

Once you enter Hyrule, walk through the marketplace to the castle. In the castle area, climb the vines on the wall, climb down the ladder to the guard house, and exit. Head towards the dead end sign, turn around, and run up the steep hill, up to the grass with a tree and butterflies. Run past the tree towards the left outer wall of the castle. Jump over the wall, then into the moat and swim past the guards until you can climb out near the tree. Talk to the sleeping guy, and head back to the marketplace.
Talk to the red-haired girl, and she'll give you an item to wake him up. Equip the item, and use it the next day on the guy.
Once he's out of the way, push both crates into the moat, climb them, and jump across to the drain. Crawl into the drain to get into the inner garden. Once here, you have to avoid the guards by hiding behind bushes and climbing up the wooden structures. Just walk very slowly over them and you'll get through.

Once past all these guards, you'll find Princess Zelda.

After you defeat The Deku Tree and leave Kokori Forest you head for Hyrule Castle. Make your way across Hyrule Feild and you will see the huge castle in front of you. Go through the town and enter the entrance at the back. On your right you will see a cliff with some vines hanging down. Walk up to the vines and press forward to climb them. When you get to the top walk until you come to the gate then jump down on the other side. You need to avoid the guards that are standing around so just follow the little yellow flower patches until you come up to a wall with some bricks sticking out that you can climb. Now you are ontop of another ledge so jump into the moat. Swim until you get to an area where you can get out. You will see a man sleeping on the ground. Go up to him and try to talk to him. He wont respond so you are going to have to wake him up by going back to where you first climbed those vines and there should be a little girl there. It's his daughter named Malon and if you talk to her she will give you an egg. Wait until dawn when the egg hatches and then go back to the sleeping man. Pull out the chicken right in front of him and he should wake up. After he moves you need to move the blocks so you can jump into that little hole you see in the wall in front of you. Now there is a series of guards patrolling this area that you have to get by but after that you will reach the princess!! Sorry this was so long but I hope it works for you. Good luck!