Before you can reach the first heart container, you need to purchase the Blue Candle. It costs 60 rupees and can be purchased at the shop just to the northwest (one screen north and one screen west) of the starting point.
Once you have it, head east one screen, north three screens, and west one screen.
Use your new Blue Candle to burn the fifth bush from the right side of the screen to reveal a hidden grotto. Inside, an old man will offer you a life potion or a heart container. Choose the heart container.
To acquire the second heart containers, you will need bombs. You can purchase these at some shops, but you can get them for free by fighting enemies. The spear-throwing Moblins often drop them. You can find Moblins in the forests located both east and west of the starting point.
Once you have bombs, head four screens east to reach the northwest corner of the ocean. Once you arrive, use your bombs on the northern rocks to reveal a secret cave. Inside, you will once again be offered a life potion of a heart container by an old man.
The third heart container is harder to reach than the first two. You will have to fight (or avoid) some harder enemies to reach it. Like the second, you will need bombs to acquire this heart container.
Move east one screen, north five screens, and east four screens to reach the mountains where the heart container is located. You will travel along the eastern side of a lake and through a desert full of Leevers (the previously mentioned “harder enemies”).
When you arrive, defeat the jumping Tektites and then place a bomb on the right side of the rock in the middle of the screen to reveal another secret cave and another old man with a heart container.
You will need the raft to collect the fourth heart container. It is hidden in level three.
When you have it, travel east eight screens and north four screens (you will pass heart container #5 on the way). Walk to the dock to travel across the ocean to a hidden area in the mountains. The area looks like a dungeon, but it is actually just a cave with an old man. Inside, choose the heart container instead of the life potion.
You will need the step ladder to collect the final heart container. It is hidden in level four.
Once you have the step ladder, travel east eight screens and north two screens. You will see the heart container in the ocean on the right side of the screen. Use your step ladder to reach it.