Once you awake and gain control of Link, hop out of bed and exit your house. If you enter the cave just north of your house, you will find your way blocked by a ledge, so for now continue north to reach Kakariko Village.
Once you reach Kakariko Village, enter the eastern door of the long house near the center of the village and break the pots inside to gather bombs. These will be very useful in one of the puzzles coming up soon, allowing you to skip a section of the Guardhouse Sewers. You should only need 1 or 2, but you can carry up to 10, and it won't take long to gather them.
Next, enter the cave directly north of the building where you found the bombs. Avoid the Beamos and make your way to the lower level and enter the next room. Open the chest in the corner in order to receive your first piece of heart.
Exit Kakariko Village to the east, being careful to avoid the guards. Once you have passed the cemetery, you should see a path above you. Follow that path to reach the Village Church
Inside the church, climb the ladder in the southeast corner to find a chest containing a heart container
Exit the church and continue south until you reach a ledge which you can jump off of. Jump down and enter the cave to the east.
Inside the cave, you will encounter an Armos Knight. Since you don't have a sword yet, all you can do is run into the room to the west, then exit to the south. Follow the cave around until you find a chest containing the lantern
Jump down the ledge and climb the ladder to exit the cave, where you will find yourself just outside your house. Return to Kakariko Village and enter the large cave found in the cliff on the north end of town