Milk Road and Romani Ranch
Leave Clock Town from the southern gate. Before heading to the Southern Swamp, if the third day has started, you can also follow the Milk Road in the southwest corner of Termina: Give life to the Owl Statue, pop Tingle's red balloon to buy the Romani Ranch map for 20 rupees (or do it later). Then continue straight on (westward on the map) and get in the ranch.
If you continue straight on (west of the map), you will discover Epona in an enclosure, but follow the path up to the Chicken House. Talk to Grog the cucco-loving who will be added to the notebook. Then use the Bremen Mask, keep the "march" button pressed and walk around to gather all 10 chicks. Once you have brought back all the chicken, Grog will give you the Bunny Hood.
If you come directly from the southern gate (and didn't go to Lon-Lon Ranch), go straight ahead, through an empty stump, then look at the drawing carved in a tree on the right. You see Tael and Tatl playing with Skull Kid, then Skull Kid grabs the Majora's Mask while the mask salesman is sleeping. Finally, go straight ahead towards the Southern Swamp.
Southern Swamp
First get rid of the bats near the first tree, then use the vines to climb it until you find a Piece of Heart. Look for Tingle's red balloon, put on the Deku Mask, pop the balloon, remove the mask and buy the map of Woodfall for 20 rupees. Then keep going straight ahead (south).
Take a few steps and check the Owl Statue on your right.
On 3DS: Here you will meet an owl who tells you about the statues he placed throughout the land to help you. Look at the notes carved in the stone and learn the Song of Soaring.
If you have a Town Title Deed, move to the pontoon a bit further, climb the ladder leading to the Swamp Tourist Centre, talk to the Business scrub on the left, and give him the Town Title Deed to get his Swamp Title Deed. Use the flower as Deku Link to glide to the roof and find another Piece of Heart.
Go east, swim towards a pontoon floating on the water, walk past a cauldron and go on towards the Magic Hags' Potion Shop. You may see a witch on a broom flying away. Go left and find a path to the Woods of Mystery.
Woods of Mystery
As Link, talk to the monkey and follow him without stopping. (Don't stop if you see a witch flying.) If you have the Bunny Hood, wear it since it will make you run faster. Talk to Koume without wearing a mask. She says that she was looking for mushrooms when she was hurt by Skull Kid and she now needs some energy.
If you play on N64 OR if you play on 3DS and that it is still the first day, leave the woods and go back to the Magic Hags' Potion Shop, get in and talk to another hag. Tell her what happened to her sister Koume. Then she gives you a Red Potion.
If you play on 3DS and it's the 2nd or 3rd day, backtrack until you see another witch flying. Target her to talk to her and tell her what happened to her sister. Kotake gives you a Red Potion.
Go back to the Woods of Mystery, find Koume by following the monkey, talk to her and give her the potion. She adds that she's the swamp tour guide and takes care of boat cruises. Leave the Woods of Mystery. If you see three monkeys when going out, follow them to the Swamp Tourist Centre. (If no monkey is waiting, go there anyway.) Get in the house, speak to Koume at the front desk on the right and she will give you the Pictograph Box along with a free boat ride. Get on the boat and get out at the first stop.