The following will guide you through Hyrule and Lorule, taking you to each of the game's dungeons.
After your conversation with Gulley, check in at the weathervane outside of Link's House - these will be used later as fast travel points. Head west to spot Gulley running north. Follow him northwest to reach the Blacksmith's House. Enter, and after a quick cut scene, the Captain will leave without his sword. Grab it off the table; it's up to you to return it.
Head to the marked spot on the map. The southern gate is blocked by a man who informs you that the Captain has actually gone to the Sanctuary. This will be marked on your map, so make your way there. Don't forget to use the weathervane out front!
After a cut scene, the Sanctuary will be locked, and you'll have yourself a sword. Move east to find a gravestone with two short trees blocking it. Slash these away, then push the stone forward to reveal the secret passage into the Sanctuary.
Down here are the Sewers. Move around the ledge to the chest in front of you; open it for the Lantern. This will make moving through the dark much easier. Light the torches at the northern end of the room to continue forward.
This is a very large, very dark room. Make your way to the left, lighting any torches you see. The light will fade after a while, but it will help you get around. Climb the stairs on the left side of the room to find a locked door by a walkway. Follow the walkway to its end to find another chest. Open it for a Small Key.
Return to the locked door and use your Small Key to move through. Inside are three Poes; take them out to open the way forward. Pull the left-side handle in the next room to open the way to the top floor.
Now in the Sanctuary, follow the hall to encounter some important characters…and villains.
Now you find yourself in Ravio's Shop, a.k.a. your old home. He'll give you his bracelet, but we'll learn about its power later. For now, you need to return to Hyrule Castle. Talk the guard by the door inside the courtyard, and you'll be beckoned by Impa.
Inside, examine each painting while Impa fetches Princess Zelda. Once Imp calls for you, head up the stairs and into the throne room. After the cut scene, you'll receive her Charm and be asked to reach Kakariko Village.
Head west to the marking on your map to reach Kakariko Village. Enter the double-doored building in the northern part of town to meet Sahasrahla. He'll task you with finding Osfala in the Eastern Palace. While you're here, you can also grab a Shield from the Item Shop for 50 Rupees.