This page explains how to complete the Anju and Kafei Quest, which is the longest sidequest in Majora's Mask. Each section lists the day and time during which you have to complete a task that is required for the Anju and Kafei Quest.
Day 1, 10AM through 12PM: Get the Kafei Mask
Go into the Mayor's residence after 10AM on the first day and go into the office to the right of the receptionist desk. Talk to the pink-haired lady on the couch to get Kafei's mask. (Note: if you already have the Kafei Mask, she won't give it again since you already have it.)
Day 1, 2:10PM to 8PM: Show Anju the Kafei Mask at the Right Time
At 1PM, the Postman goes into the Stock Pot Inn in East Clock Town. Go there and watch him give Anju a letter. Then when the Postman is leaving, put on the Kafei Mask and talk to Anju. She will ask you to meet her in the inn at 11:30PM tonight.
Optional: Day 1, 2:10PM to 3:50PM: Get the Room Key
Optionally, you can talk to Anju after the Postman gives her the letter, but don't wear the Kafei Mask. Anju will give you a room key. You can use it to enter the Stock Pot Inn at night. If you don't talk to Anju before 3:50PM to get the room key, a Goron will come in and get the key instead.
Day 1, 12AM to 6AM: Meet Anju in the Inn at Night
Go into the Stock Pot Inn at midnight on the first day. If you got the room key as described above, you can just go in through the front door. If you didn't get the key, become a Deku Scrub and use the flower near the Stock Pot Inn entrance to float up and onto the roof over the front of the Inn, then go into the door up there.
Go to the Inn's kitchen and wait for Anju to arrive (around midnight). Talk to her and she gives you a Letter to Kafei.
Day 2, 6AM to 9AM: Mail the Letter to Kafei
Wait until after the Dawn of the Second Day, or play the Song of Double Time to get there right away. Put the Letter to Kafei in any mailbox. This must be done before the 9AM on the second day.
Day 2, 3:10PM to 3:50PM: Go into the Laundry Pool Hideout
Before 3PM on the second day, go to the Laundry Pool. The postman goes there at 3PM with the Letter to Kafei. After he rings the bell, go into the door that the masked kid just came out of. Wait in there until the masked kid comes back in.
Day 2, 4:10PM to 6PM: Talk to the Masked Kid
Talk to the masked kid when he comes back into the Laundry Pool hideout. As you might have guessed, the masked kid is Kafei. He's actually an adult, but the Skull Kid turned him into a kid. Kafei says that the prancing man from North Clock Town stole his wedding mask. Kafei gives you the Pendant of Memories.
Day 2 or 3, 10AM to 7PM: Give Anju the Pendant
Give Anju the pendant to convince her to stay in town and wait for Kafei.
Day 3, 1PM to 6PM: Receive the Special Delivery
Go into the Laundry Pool Hideout where you first met Kafei. The Curiosity Shop Owner is there instead. Talk to him to get the Keaton Mask and the Special Delivery to Mama (or just the Special Delivery if you already have the Keaton Mask).
Day 3, 6PM: Get the Stolen Mask
Warp to Ikana Canyon and go to Sakon's Hideout. Kafei will be hiding behind a rock near the entrance. Hide with Kafei. You can wear the Stone Mask to prevent Sakon from noticing you. If you don't have the Stone Mask, make sure you are behind the big rock so Sakon won't see you, because if he sees you, you won't be able to get into the hideout. If you want to be sure that he doesn't see you, raise your shield (hold R) while standing behind the rocks. Eventually Sakon prances into his hideout. When Kafei goes into the hideout, follow him.
Go into the door straight ahead. It locks behind you. Watch the cut scene.
Afterward, step on the switch that Kafei asked you to step on. You'll switch to Kafei.
You and Kafei need to work together to reach the last room before the Sun Mask falls into the hole and ends up back in Sakon's hands.
As Kafei, go through the door, then push one of the big blocks onto the switch in the middle.
As Link, go through the door to the left. Kill the Deku Baba in this room.
Then as Kafei, go through to the next room. Stepping on the yellow switches slows the conveyor belt. Don't step on the red switches because they speed up the conveyor belt (temporarily). When you are ready, step on the blue switch in the bottom-right corner.
As Link, go through the door that opened. Kill the two Deku Babas in the next room.
As Kafei, go through to the next room. Push the leftmost block down, then step on the yellow switch and pull the block that is to your right, making it cover the yellow switch. Then go around and push the middle block down onto the blue switch.
As Link, go to the next room. Kill the Wolfos that appears.
As Kafei, push the rightmost block out of the way of the door, then go to the next room. Step on the blue switch in there. As Link, go to the next room and step on the other blue switch. If you made it in time, Kafei gets the Sun Mask back. After Kafei runs back to town, it is now midnight on the third day. Warp to Clock Town.
Optional: Day 3, 6PM or later: Give Mama the Special Delivery
At this point, you can get a Piece of Heart or a new bottle with Chateau Romani milk in it. To get both, you have to do the quest twice.
To get a new empty bottle, wear Romani's Mask to enter the Latte Milk Bar, which is next to the Stock Pot Inn. Talk to Madame Aroma while wearing Kafei's Mask. Give her the Special Delivery to get a new bottle that is filled with Chateau Romani milk.
To get the Postman's Hat instead, go into the Post Office in West Clock Town and give the Special Delivery to the postman. Follow him to the Latte Milk Bar, which is next to the Stock Pot Inn. Wait for him to come back out and stand by the wall, then talk to him. He gives you the Postman's Hat.
Day 3, 6PM or later: Watch Anju and Kafei's Reunion
Go into Anju's Room at the top of the stairs in the Stock Pot Inn. Then wait. When there is 1:30:00 left on the countdown, watch the cut scene and you will receive the Couple's Mask. Use the Song of Time to save and go back to the Dawn of the First Day.