Each ending is determined by what responses you choose when recalling what you replied to Aya's letter with.
The endings are:
The Cursed Letter
The Princess of Himegamori Forest
A Government Plot (unlocks after first playthrough)
Crossing Paths
The Bond of Marriage (unlocks after first playthrough)
Since The Bond of Marriage is considered the true ending, it's recommended you do this one last. It doesn't really matter what order you do the endings in, though.
Also note that the replies for Chapter 3's letter won't pop until a few minutes into the chapter.
Cursed Letter replies
Chapter 1: The First Letter
Reading
Do you like to read?
Chapter 2: Dragonfly Stationery
I think I’d like to explore old ruins
Are there any spooky stories about Shimane?
Chapter 3: Banana Stationery
I don’t want to become an adult
Do you want to become an adult soon?
Chapter 4: Candy Stationery
Girls seem self-centered
What do you think of your own personality?
Chapter 5: Gal Stationery
Nature
Do you believe in ghosts?
Chapter 6: Ginger Stationery
Long, black hair is beautiful
Do you like black hair?
Chapter 7: Gnome Stationery
Right now I enjoy doing stuff with friends
Where do you hang out with friends?
Chapter 8: Magatama Stationery has no letter replies and cannot be skipped.
If you got the route correctly, Chapter 9: Crow Stationery should start up.
The Princess of Himegamori Forest replies
Chapter 1: The First Letter
Walking Around the Shrine
Do you like folklore?
Chapter 2: Dragonfly Stationery
I think I’ll research history
Where there any famous warriors from Shimane?
Chapter 3: Banana Stationery
I don’t want to have ideals
What do you think of selfish adults?
Chapter 4: Candy Stationery
I like girls
Aya, what do you think about history buffs?
Chapter 5: Gal Stationery
Ancestors
What kinds of times do you enjoy?
Chapter 6: Ginger Stationery
Mysterious and beautiful people
Are you interested in studying folklore?
Chapter 7: Gnome Stationery
Right now I’m concentrating on studying
How do you study history?
Chapter 8: Magatama Stationery has no letter replies and cannot be skipped.
If you got the route correctly, Chapter 9: Mirror Stationery should start up.
A Government Plot replies
(unlocks after playing through the game once)
Chapter 1: The First Letter
Go for a Walk
Do you believe in aliens?
Chapter 2: Dragonfly Stationery
I think I’d like to see a meteor shower
Is there a good view of the starts in Shimane?
Chapter 3: Banana Stationery
My ideal adult is rich
Do you like rich people?
Chapter 4: Candy Stationery
I don’t care about gender or nationality
Do you like aliens?
Chapter 5: Gal Stationery
Money
Are you interested in making money?
Chapter 6: Ginger Stationery
Girls with nice figures
Please tell me your measurements
Chapter 7: Gnome Stationery
I can’t focus myself
Where do people go on dates in Matsue?
Chapter 8: Magatama Stationery has no letter replies and cannot be skipped.
If you got the route correctly, Chapter 9: UFO Stationery should start up.
Crossing Paths replies
Chapter 1: The First Letter
Go Play
Do you like sports?
Chapter 2: Dragonfly Stationery
I think I’d like to participate in a school function
What kinds of events are popular in Shimane?
Chapter 3: Banana Stationery
My ideal adult is someone who has dreams
What kind of adult do you want to become?
Chapter 4: Candy Stationery
Friendship between men and women is wonderful
Do you think men and women can be friends?
Chapter 5: Gal Stationery
Kindness
Tell me about your personality
Chapter 6: Ginger Stationery
People who are fun
What kind of people do you like?
Chapter 7: Gnome Stationery
There’s someone in my mind
Aya, is there someone you like?
Chapter 8: Magatama Stationery has no letter replies and cannot be skipped.
If you got the route correctly, Chapter 9: Rain Stationery should start up.
The Bond of Marriage replies
(unlocks after playing through the game once)
Chapter 1: The First Letter
Go on a Day Trip
Do you like traveling?
Chapter 2: Dragonfly Stationery
I think I’d like to take on different challenges
Is there some challenge you’d like to take on?
Chapter 3: Banana Stationery
My ideal adult is my dad
Aya, what’s your ideal adult?
Chapter 4: Candy Stationery
Men and women can be friends
Is there someone you’ve let into your heart?
Chapter 5: Gal Stationery
Encounters
Have you had any special encounters?
Chapter 6: Ginger Stationery
People with complementary personalities
Do you believe in destiny?
Chapter 7: Gnome Stationery
I have feelings for you, Aya
I want to know more about you I guess
Chapter 8: Magatama Stationery has no letter replies and cannot be skipped.
If you got the route correctly, Chapter 9: Blue Sky Stationery should start up.
The trophy should pop as soon as you finish your last ending.