After you've found the letter, you can go to one of the many Potion Shops and purchase a Blue or Red Potion. Most of them are in the same location in both quests, but a few are different.
Location: From the start screen head right 1 screen, up 5 screens, right 5 screens, up 1, right 1, and up a screen.
Description: The old man in the cave here will give you a letter to show to the old woman. After showing it to her, all potion shops throughout Hyrule are now open.
Location: Exit the graveyard to the right and continue right another screen. Head up along the right side, right 2 screens, up 1, right 2, up 1, and left 3 screens.
Location: Exit the graveyard to the right and continue right another screen. Head up along the right side, right a screen, up 1, left 1, up 1, left 2, and down a screen.
Uncover: Use the Power Bracelet to push the block on the left down. This will reveal a staircase where the Old Man is located.
Description: The old man here will give you a letter to show to the old woman. After showing it to her, all potion shops throughout Hyrule are now open.
Location: From the start screen head right a screen, up 5 screens, left 1, up 1, and right a screen.
Uncover: The cave is actually against the rocks above the water. Place a bomb on the far right side of the screen to reveal this cave. You will need the ladder to reach this location.
Location: Exit the graveyard to the right and continue right another screen. Head up along the right side, right 2 screens, up 1, right 2, up 1, and left 3 screens.
Location: Exit the graveyard to the right and continue right another screen. Head up along the right side, right a screen, up 1, left 2, and up a screen.
Uncover: Place a bomb against the rocks just right of the staircase to reveal a cave.