Once you have left the Moon Labyrinth, get as many free container hearts you could via usage of bombs and the blue candle.  One is in a forest, another is on the south shore in a cave, and one is just west of the east shore in a cave one scene left to the northeast.

Next, find as many of the secret coin places.  Two are under Armos, both near the same place.  Then get the Letter.  The letter is just north of the northern shore on the northeast-corner of the world.  The letter is required for Link to purchase medicine later in the game.

Then go for the White Sword.  The requirement for the white sword is for Link to have a life gauge of 5 container hearts and have the Magic Shield.  The White Sword is located on top of the waterfall just west of the Lost Hills.

Next, get 250 rupies by trying to get as many free rupies as possible (there is one location east of the Lost Forest where 100 rupies is given out), while destroying creatures at the same time.  Once the 250 rupies have been obtained, go to a scene west of the lake that should have six Armos.  Bump into the second upper Armos in that set of six and get the Blue Ring.

Now go into the cave that is west of the bridge and show the lady the Letter. From that point on, you will be allowed to buy medicine, sold at 40 and 68 rupies.  It is more economical to buy the Red medicine jar for 68 rupies, as it can be used twice unlike the blue one.

Once that is done, you are now ready for the Manji labyrinth.