There are a few things you could do in the Graveyard, with the first thing on the list being obtaining the Sun's Song. Since you have an Empty Bottle, assign it to a slot, pick up the rock near the entrance and swing the bottle at the bugs that come out. Keep these for later and go to the back of the Graveyard, to the big tombstone. Take out your Fairy Ocarina and play Zelda's Lullaby while standing on the Triforce symbol, which will cause the tombstone to explode, revealing a hole.
Drop down into the hole to appear in the Royal Family's Tomb. In the first room is a new enemy, Keese, which you have to kill four of to open the door. Go through the door, where you'll find another new enemy, the ReDeads. These enemies will freeze you in your place if they look at you, and they can jump on your backs, draining your health.
Go along the left side of the room and through the opening on the other side. Inspect the stone in this room to learn the Sun's Song, which will change the time of day from day to night, and vice versa when played. Go back to the previous room and play the Sun's Song, which will temporarily stun all of the ReDeads in the room. Exit the tomb to get back to the Graveyard.
LOOTING THE GRAVES
There are two graves you can pull back, which will reveal holes that you can drop down into and find some items. For the first one, pull the fourth grave (top row) from the left back and drop down. Inside, you will find a small room with a ReDead, so use the Sun's Song to stun it, then kill it. Stand on the pedestal and play the Sun's Song again, which will make a chest appear, with a Piece of Heart inside.
Exit back to the Graveyard and find the grave with the grass in front of it. Pull it back to reveal another hole, and drop down inside. There is a little chest here that will give you a Hylian Shield, for free! If you wanted it normally, you would have to pay 80 Rupees at the market in Hyrule Castle Town (60 with a discount).
