It's really easy to get this sword. It doesn't cost you a thing to get the white sword. The white sword has twice the power as the wooden sword. The wooden sword is the first sword you get at the beginning of the NES Nintendo Legend of Zelda game.
The only requirement you need to get the white sword is five heart containers. If you go to the old man prior to that, he will not give the sword to you. You can obtain additional heart containers by completing levels and finding them throughout hyrule. A heart container guide is available through this website.
From the beginning of the game, go east one screen. Now go north five screens. From here go west one screen and then north one screen. From there, go east three screens. You'll now see a staircase heading north.
Take the staircase north and you'll see a cave entrance. Before you get into the cave a Zora will be firing shots at you and another blue enemy will be throwing swords at you. Dodge the blue sword throwing enemy until he is out of the path, then make a mad dash for the cave entrance.
Go inside and the old man will give you the white sword.
