A few times each season, the villagers will gather together to celebrate and compete with each other. The festivals give you a chance to interact with the people of Chestnut Town as well as raise your friendship Music Notes with them.
Spring 10 - Flower Festival
On this day give flowers to the villagers. Giving a favorite flower will increase your friendship a large amount (1 Music Note) compared to if you gave any other type of flower (1/2 Music Note). Some of the flowers they prefer are mutations of the regular version, which you might not have on-hand for your first festival (e.g., Pink Carnation is a Fall mutation of Red Carnation, and Viola is a Winter mutation of Purple Pansy, which is a Winter mutation of Purple Pansy).
The villager favorite flowers are:
Andrea: Red Rose
April: Pink Carnation
Blossom: a pink flower
Brutus: Purple Pansy
Catherine: White Rose
Dewy: a blue flower
Emily: Yellow Tulip
Gilbert: White Dahlia
Hanna: Yellow Pansy
Harvest God: Blue Rose
Harvest Goddess: Tulip
Iris: Pink Pansy
Luke: Yellow Dahlia
Naomi: Pink Rose
Rowan: a yellow flower
Sally: White Tulip
Sam: Pink Dahlia
Tabitha: Sunny Red
Spring 23 and Fall 23 - Cooking Festival
On the day of the festival, talk to Hanna in the town plaza between 10:00 am and 2:00 pm. You may enter one dish into the festival. The category of dish does not matter, and it does not need to be a dish that you have cooked; for example, it could be something in your bag that you received from unlocking a memory. After you submit your entry, Hanna will make her judgment and declare the winner.
If you win you'll be rewarded with an ore.
The contest will be over at 5:00 pm.
Summer 12 - Fireworks Festival
On Summer 4, Rowan will let you know about the upcoming festival and recommends that you talk to a marriage candidate to invite him/her to watch the fireworks. Between the 5th and the 11th, talk to a bachelor (if you're playing as a girl) or a bachelorette (if you're playing as a boy) to invite the person to view the fireworks with you.
To trigger the festival, walk into your farm house between 5:00 pm and 8:00 pm on the 12th of Summer. The two of you will head up to the mountain to watch the sky light up. You'll then return back to your farm house at 9:00 pm.
You'll earn about a half-note of friendship with the person you invite.
Summer 23 and Winter 23 - Fishing Contest
Sam will stop by your house in the morning to invite you to participate in the Fishing Contest. Talk to him in front of his booth from 10:00 am to 3:00 pm to enter into the contest. Before 10:00 am and even during the entry time, Sam will not be available in vendor mode to sell you fish bait. Remember to buy fishing bait from him the day before the Fishing Contest if you plan to use it.
Once you've enter the contest, you will have until 4:00 pm to catch as many high value fish as you can. The points you earn is based on the size of the fish that you catch. Larger fish will earn you more points. Using bait will help to increase the maximum size of the fish you catch, so it is well advised to use Good Bait or Excellent Bait when competing in this festival.
The contest will end at 4:00 pm. If you are declared the winner, you'll receive 6 high-tier crop mutation seeds such as Golden Pepper or Dryad.
Fall 30 - Fall Festival
This minor festival is where you will be giving cooked food to your marriage candidates. Giving cooked food to the regular villagers won't trigger special dialog, and giving non-cooked dishes, such as eggs, flowers, or vegetables, to the marriage candidates will just trigger typical "thank you" responses.
You can buy cooking recipes from Hanna while she is running her Restaurant during the day. Then use your kitchen to make the dishes you wish to give. Any cooked dish will generate a festive response when you give it to the marriage candidate.
Winter 25 - Starry Night Festival
On this festival you can invite someone to watch the stars with you at night. Talk to a marriage candidate to ask the person out for the evening. Then on the 25th, walk into your house between 5:00 pm and 8:00 pm. The two of you will walk up to the mountain to watch the stars.
If you are married, your spouse will request that you return home between 5:00 pm and 8:00 pm.
Winter 30 - New Year's Eve
If you're married, your spouse will ask that you return home between 9:00 pm and 12:00 am. Once inside, the two of you will have dinner