What do I do with this monkey I have found?

You can feed them, pick them up, and talk with them, eventually befriending them.

When you become really good friends with the certain wild animals, entering their area will trigger a gift event.

The wild animal family will give you 10 of a certain item based on the animal family you befriend. By befriending a wild animal of a particular color, you might unlock another different colored one of the same family (which you can also befriend) or something else....

Here is an updated list of wild animal likes and gifts translated from this wiki.

Likes/Gifts (wild animal are available all year unless otherwise noted, gifts are in sets of 10, unless otherwise noted):

• Duck (Spring/Summer) (Sunny) (River) (Morning to Midnight)

  Likes: All vegetables (except onions and spinach), all fruits, soybeans, wheat, rice

  Gives: Basil

• Duck (Alternate) (Winter/Fall) (Sunny) (River/Sakura Land) (Morning to Midnight)

  Likes: All vegetables (except onions and spinach), all fruits

  Notes: Unlocked by befriending Duck

  Gives: White Rose

• Brown Boar (Snow/Sunny) (River/Summit/Forest) (Morning to Evening)

  Likes: Eggs, golden eggs, Silkie eggs, mushrooms, king oyster mushrooms, shiitake, pineapple, apple, kiwi, orange, peach, watermelon, banana, strawberry, corn, radish, cabbage, potato, carrot, tomato, potato, turnip

  Gives: Pink Rose

• Black Boar (Snow/Sunny) (River/Forest) (Morning to Evening)

  Likes: Same as Brown Boar, except Coral Mushrooms instead of Silkie eggs.

  Notes: Unlocked by befriending the Brown Boar.

  Gives: Nadeshiko

• Black Rabbit (Spring to Fall) (Sunny) (River) (Morning/Noon to Evening)

  Likes: Fodder, grapes, cherries, pineapple, apple, banana, strawberry, corn, broccoli, cabbage, pumpkin, cabbage, potato, carrot, tomato, potato, turnip

  Gives: Tulip

• White Rabbit (Fall/Winter) (Snow) (Summit) (Noon to Evening/Midnight to Morning)

  Likes: Same as (Black) Rabbit.

  Notes: Unlocked by befriending the Black Rabbit

  Gives: Lavender

• Brown/White Ermine (Sunny) (River, Summit, Forest, Snow Land [White]) (Day)

  Likes: Eggs, golden eggs, Silkie eggs

  Notes: White Ermines are only available in Snow Land

  Gives: Chamomile (Brown), Margaret (White)

• Yellow Fox (Spring/Summer) (Snow/Sunny) (Forest) (Noon to Evening, Midnight to Morning)

  Likes: Eggs, golden eggs, Silkie eggs, All mushrooms (except shiitake), all vegetables (except onion and spinach)

  Gives: Rosemary

• Silver Fox (Fall/Winter) (Snow/Sunny) (Forest) (Noon to Evening, Morning)

  Likes: Same as Yellow Fox

  Notes: Unlocked by befriending Yellow Fox

  Gives: Red Rose

• Brown Bear (Spring to Fall) (Sunny) (River/Summit/Forest) (Morning to evening)

  Likes: Honey, all vegetables (except spinach and onion)

  Gives: Sage

• Black Bear (Spring to Fall) (Sunny) (River/Forest) (Morning to evening)

  Likes: Same as Brown Bear, but also salmon and alcohol

  Notes: Unlocked by befriending Brown Raccoon

  Gives: Hydrangea

• Brown/Gold Monkey (Spring/Summer) (Rain/Sunny) (Forest/Summit/River/Southern Island/Ruins) (Morning to evening)

  Likes: All vegetables (except spinach), all fruit, lotus root, wasabi, soybeans, all mushrooms, all cheese, eggs, golden eggs, Silkie eggs

  Notes: Gold Monkeys are unique to the Ruins

  Gives: Bayleaf (Brown), Gerbera (Gold)

• Brown/Olive Sparrow (Sunny/Snow/Rain) (Summit, River, Forest, Sakura Land) (Morning to evening)

  Likes: Corn, wheat, rice, soybeans

  Notes: Olive sparrows are only available in Sakura Land during the day

  Gives: Mint (Brown), Thyme (Olive)

• Brown Raccoon (Rain/Sunny) (River/Summit) (Day)

  Likes: All vegetables (except spinach), all fruit, eggs, golden eggs, Silkie eggs

  Gives: Bergamot

• Dark Brown Raccoon (Spring/Summer) (Sunny) (River) (Evening to morning)

  Likes: Same as Brown Raccoon

  Notes: Unlocked by befriending Brown Raccoon

  Gives: Gentian

• Panda (Sunny) (Forest) (Night to Morning)

  Likes: Bamboo, wheat, rice, grapes, banana, strawberry, corn, cabbage, potato, carrot, tomato, potato, turnip

  Notes: Wild animals that inhabit the River/Summit/Forest might also appear

  Gives: Sunflower

• Turtle (Southern Island only) (Day)

  Likes: All fish

  Notes: Once you become friend it can take you to the Southern Island (unlocks area so you don't have to use the Travel Agency)

  Gives: Aloe

• Yeti (Snow Land only) (Day)

  Likes: All vegetables (except spinach), all fruit, all fish

  Personal Note: Yetis are cool

  Gives: Snow Drop

• Polar Bear (Snow Land) (Day)

  Likes: All fruit, all fish

  Gives: Blue Rose

• Peacock (Ancient Ruins only) (Daytime)

  Likes: Soybean, wheat, rice, all vegetables (except spinach)

  Gives: Pink Diamond (x1)