COWS
You start out the game with one cow that can give you milk to start earning money. You can buy more if you wish.
They eat fodder and good fodder. You start out with some fodder. You should feed each cow 1 unit of fodder each day or you will run out very quickly! The cow should also be milked once a day! You can either use the milker or your hands, it doesnt really matter. Make sure to buy your cow the animal medicine when he/she gets sick or it will die. To make your cow give birth make sure you have a male and female cow in the barn and use the Miracle Potion which you can find in the ledger.
HORSES
Takakura will give you a horse somewhere in the middle of the first part of the game.
They eat fodder, feed them once every 2 days or you will run out very quickly, the horse never needs the animal medicine. The horse also does nothing for you except stand around. You can ride him all over Forget Me Not Valley though!
GOATS
Basically the same as a cow.
CHICKENS
You can buy these for 900G
They eat Bird Seed, feed them when their food runs out, which takes a couple of days. And check under the chicken every day to see if there is an egg under it. Thats just about it.
It is basically the same as the cow