Inside the deku tree
Getting the slingshot
Take note of the spider web one the floor, you'll need to use it later. Defeating the enemies around will yield Deku Nuts. Climb up the vine and head right, there will be a chest containing the map. After you get the map, head into the door up the path. Use your shield to reflect the nuts back at the monster. After you hit him once, he will get up and run away, chase him. He will tell you a secret in exchange for his life. You have no options, so he lives another day. In the next room, you will have to be quick. Jump across the platforms to get your Slingshot. After this, go ahead and shoot down the ladder directly in front of you.
Getting through the spider web
Now get to the chest where you got the map from and shoot the spiders with your slingshot. Make your way up the vines and head right. Ignore the big spiders for now. Enter the door. Jump on the button near the lit lantarn to bring up 3 platfoms. Jump on the platforms and make your way to the end of the room. Open the chest to find the compass. Jump down and use the vines to get to the beginning of the room. Equip a deku stick and hold it in the lit lantarn. When the deku stick is lit walk to the lantarn near the vines and light it. The closed door will open. Head throught the door.
Walk towards one of the three openings in the spider web. A big spider will come down from the ceiling. Strike it with your sword when it has his back pointed at you. Now you need to jump towards the floating recovery heart. If you do this correctly you will fall through the spider web.