The Adventure of Link Heart Containers
A total of four Heart Containers can be found all over Hyrule. They will increase your overall life meter a little each time you find one.

Western Hyrule

Heart Container #1 Parapa Desert
 - Go straight south from the first palace (Parapa Palace), through a small valley. You will encounter a cut scene where you must jump over water pits and avoid bubbles. The road will lead to a small forest with a small area of grass in the middle, walk over the grass to encounter a Goriya and the Heart Container.

Heart Container #2 Midoro Swamp Cave
 - The Hammer is required on getting this Heart Container. Once you have the Hammer, take out the rock just south of the town of Rauru. Next, take out out the rock blocking the cave to the right, and enter the cave. Follow the cave to the end to eventually find the Heart Container.

Eastern Hyrule

Heart Container #3 Ocean
 - You must obtain the Boots to acquire this Heart Container. Once you have the Boots, walk out into the sea (past the town) like you were going to the palace, but instead find a hidden path that will lead you just north of the palace to find the third Heart Container.

Heart Container #4 Southeastern Hyrule
 - The fourth Heart Container is near the east beach next to the sixth palace (Third Eye). Walk along the edge of the beach until you find the hidden spot where the last Heart Container is.