Before embarking on this quest, I recommend a few things first. Firstly, while human, tell the boy in East Clock Town the code to the Bombers' Hideout and return to the observatory. Don't bother with the Moon's Tear, but instead speak to Bonooru, the scarecrow at the base of the Astral Observatory (alternatively, he can be found in the Trading Post, but we need the Notebook from the Observatory as well), and teach him a song. Ask him to teach you the songs that slow down time and speed up time. If you've taken awhile to get this done, I recommend you do the following instructions and then return to the dawn of the first day and use the Inverted Song of Time to have the maximum possible to complete Woodfall Temple.
After learning the two additional time songs, exit the hideout from the entrance you used (while human). Jim, the leader of the Bombers, should approach you and give you the Bombers' Notebook. Excellent. Now, I recommend saving and returning to the first day using the Song of Time, and then using the Inverted Song of Time immediately upon exiting the tower, which will double the approximately 72 minutes the game gives into approximately 144). Now that we have the notebook and the extra songs for altering time, let's head to the swamp.
The Southern Swamp
Southern Termina Field
So, let's start saving the princess and the monkey by getting to the swamp. Head south (past the carpenter's tower in South Clock Town from Clock Town. You should see a lot of green, and a large tree at the entrance to the swamp directly south from Clock Town. When you reach the tree and see the handmade drawing of Skull Kid, Tatl, and Tael, Tatl will begin a cutscene about how she and her brother befriended Skull Kid. At the slightly ambiguous end of that scene, head into the Southern area. Here's a grassy area with some Wolfos, and bats. Fight your way through to the opposite end of where you came in. Note that Tingle is also found here, so shoot him down with Deku bubbles to buy a cheap map of the Southern Swamp if you desire.
Magic Hags' Potion Shop
So, now that you've reach the swamp, you're going to need to start hopping on the green lily-pads left of the Swamp Tourist Center or swimming through the water to reach the Magic Hags' Potion Shop. Enter the shop, and speak to Kotake while a human. She'll tell you her sister Koume went into the Woods of Mystery to pick some mushrooms, but that she's a bit late getting back. Time to explore the Woods of Mystery. Exit the shop and run into the entrance somewhat behind the shop.
Woods of Mystery
When you walk into the Woods of Mystery, speak with the monkey. He'll tell you to follow him. Kindly oblige, but be wary: he runs quickly, and often fakes running through entrances, which will take you back to the beginning. You'll also encounter Snappers, but do not pause to fight them; the monkey will not wait for you. When you finally reach the end of the maze, you'll find Koume. She tells you Skull Kid attacked her, and that she needs something that will replenish her energy. Run out of the woods.
Potion Shop again (Empty Bottle 1)
Woods againFollow the monkey again, being wary of the Snapper turtles, and give Koume the red potion. She'll be re-energized and fly off. Time to leave once more.
Swamp Tourist Center
Now that you've freed Koume (who conveniently works the boat ride at the Swamp Tourist Center), you can take a free ride on the boat cruise, which will take you straight through the Bigocto to the Deku Palace. Now begins the second half of preparing to enter Woodfall Temple.
Please note that all purple water in and around the Deku Palace (including Woodfall itself) is poisonous and will harm Link half a heart every second. Take care not to touch the water as a human (use your light Deku figure and water lilies to bounce across the water to safety).
The Deku Palace will be a bright wonder of orange shades, but disregard and enter through the small door led by the monkey. You'll see two Deku guards and a very menacing-looking fortress. For now, you're going to turn Deku, hop across the bridge, and speak with the guards. Seeing that you're a Deku, they will permit you to visit the King's Royal Chamber to see the "public humiliation of the foolish monkey who angered our king."
Speak with the Deku inside the Chamber if you please, as they'll give you tidbits of information, and take care to speak with the Deku Butler who is sympathetic towards the monkey. After you've seen the monkey, return to the corridor behind the guards that leads to the gardens. The monkeys should approach you and ask how the imprisoned monkey is. They'll tell you that they know a secret passage to get to the monkey's jail cell (for lack of a better term). You'll need a Magic Bean from the Bean Seller to reach the passageway, however, so let's get that now.
Inner and Outer Palace Gardens
Back in the outdoor corridor, when you're facing the door to the king's chamber, the door you need to take is on the left. If you're facing the two Deku guards, the door is on your right-hand side.