The first dungeon, often referred to as 'The Eagle' due to its map shape, is located in the eastern part of the Overworld, just a few screens north of the starting cave. To find it, head one screen north from the starting cave, then one screen east, and finally one screen north again. You'll see a large, tree-covered area with an entrance resembling a cave mouth. This is your first major challenge.
Before entering, ensure you have at least 50 Rupees. You'll need them to purchase the Blue Candle inside. If you're short on Rupees, defeat some Octoroks and Tektites in the surrounding area. Once inside, prepare for your first encounters with Stalfos and Goriya. The Wooden Sword is sufficient, but careful movement and timing are key. This dungeon will introduce you to locked doors, requiring keys, and the concept of using items to solve puzzles.