If your not happy with your Wooden Sword, (The Old Man is very displeased... -.-) there is a way to get the White Sword early. This sword deals double the damage of your Wooden Sword, making the first few dungeons alot easier. From the starting screen, head right eight screens, and up one screen. Make sure to collect at least 20 rupees along the way by killing monsters. Once you have the 20 rupees, head into the cave. After the shopkeeper greets you, walk over the bombs. After you've acquired the bombs, head down one screen, and left four screens. There should be a pathway there. on the left side of the path there should be a horizontal wall the cuts of diagonally. bomb the horizontal section of this wall. walk in, and claim your Heart Container! After you leave, head up fve screens, and right one screen. In this area, you should see a bunch of tektites wandering about. Ignore/Kill them, and bomb the southern face of the huge boulder in the middle of the screen. Walk in and claim another Heart Container!
If you're following this Hint from the beginning of the game, you should now have five Heart Containers. This means you can claim the White Sword! To do this, walk right one screen, up one screen, left three screens, and up the big staircase. Avoid the Blue Lynel, and walk into the cave. As you walk in, the Old Man will say: "MASTER USING IT, AND YOU CAN HAVE THIS". What he means by this is get two heart containers from the first two dungeons. Since you got two secret heart containers, you can grab the White Sword without too much work!