You don't need to do anything about these quests to complete them. Just accept them from Simon and they'll be completed along with your Daytime Activities. Take note that Day Quests will take up one slot of your Daytime Activity so make sure to check them so you can change the plans according to which skill point you want to earn alongside the quest completion. On top of the indicated rewards, Day Quests also give skill points and unlock additional Daytime Activities.
Food is Everything 1
Giver: Glenn
Reward: 570 Libra
Food is Everything 2
Giver: Glenn
Reward: 860 Libra, Nutcracker x1
Into the Wild 1
Giver: Max
Reward: 560 Libra
Into the Wild 2
Giver: Max
Reward: 860 Libra, Vampire Bat
Relaxing Garden 1
Giver: Lily
Reward: 545 Libra
Relaxing Garden 2
Giver: Lily
Reward: 835 Libra, Mugwort x1
Timid Novelist 1
Giver: Dodgson
Reward: 180 Libra
Timid Novelist 2
Giver: Dodgson
Reward: 275 Libra
Timid Novelist 3
Giver: Dodgson
Reward: 540 Libra, French Doll x1
Cute Critters 1
Giver: Natalia
Reward: 550 Libra
Cute Critters 2
Giver: Natalia
Reward: 850 Libra, Rabbit's Foot
Joy of Gluttony 1
Giver: Marcia
Reward: 2050 Libra
Joy of Gluttony 2
Giver: Marcia
Reward: 2880 Libra
Find the Parents
Giver: Scott
Reward: 950 Libra
Save the Flowers!
Giver: Ferris
Reward: 1020 Libra
Happy Bird
Giver: Laila
Reward: 980 Libra
Sketch Life 1
Giver: Rob
Reward: 550 Libra
Sketch Life 2
Giver: Rob
Reward: 830 Libra, Mana Droplet x1
Darling's Bad Mood
Giver: Fred
Reward: 1050 Libra
Painting's Wings 1
Giver: Layla
Reward: 1000 Libra
Tourist Spots 1
Giver: Aaron
Reward: 160 Libra
Tourist Spots 2
Giver: Aaron
Reward: 240 Libra
Shop for Me 1
Giver: Ethel
Reward: 576 Libra
Shop for Me 2
Giver: Ethel
Reward: 864 Libra
Helpful Arnice 1
Giver: Isabel
Reward: 575 Libra
Helpful Arnice 2
Giver: Isabel
Reward: 970 Libra
Helpful Arnice 3
Giver: Isabel
Reward: 1200 Libra, Locket x1
Help Me Move 1
Giver: Kenneth
Reward: 1056 Libra
Help Me Move 2
Giver: Kenneth
Reward: 1584 Libra