Upgrading Link's sword is one of the most significant power boosts you can achieve in The Legend of Zelda. The Wooden Sword is sufficient for the early game, but you'll soon need more power to tackle tougher enemies and later dungeons. There are two powerful sword upgrades available: the White Sword and the Magical Sword.
The White Sword
To obtain the White Sword, you must have at least 5 Heart Containers. Once you meet this requirement, head to the screen one north and one west of the starting cave. You'll find a cave entrance. Inside, an Old Man will grant you the White Sword, which is twice as powerful as the Wooden Sword. This upgrade is highly recommended before attempting Dungeon 4.
The Magical Sword
The ultimate sword upgrade, the Magical Sword, requires you to have a full 12 Heart Containers. Once you have all 12 hearts, head to the Death Mountain region. Navigate to the screen with the three armos statues (Lost Hills). From there, head one screen north. You'll find a cave entrance. Inside, an Old Man will bestow upon you the Magical Sword, the most powerful weapon in the game. This sword is essential for the final dungeons and the battle against Ganon.