The barn:
   
Smells like a petting zoo

The barn: Animals, Feeding, and Pasture.

Animals

You start out with a cow. You can buy sheep (male only), Chickens (male/female), ducks, and a Goat. You choose between two dogs at the start of the game, and Romana can give you a cat. Takakura gives you a horse. Basically, that's it.
Because the cat, ducks, and goat don't come til' Chapter 2, I'll give you the run-down on the rest.

Dog:
Pointy-eared or Long-eared? Your choice. He lives in the small doghouse on the side of your house. Feed him if you want; it's not required.

Cows/Bulls: You start out with one female, and you can milk it til' winter. Cows only give milk a certain amount of days after giving birth (quote Takakura), so you either have to order a Bull or a miracle potion, wait an amount of days, get a new calf, and milk her again. Not that complicated.

Sheep:
Sheep are very delicate. They require "cuddling" every day, and their wool can sell for a high price-if you know how. Wash it everyday, and every month you can shear it off (using shears). If you washed and loved it enough, you'll get Golden Wool that sells for 600g at Van's shop.

Horse:
Takakura orders it for you during Chapter 1, and you'll be glad he did. It takes half the day to get from Vesta's farm to Romana's Mansion, but with the Horse, it's less that half of that time!

Chickens: (see CHICKEN COOP)

Cat: If you befriended Romana, she'll give you a cat during Chapter 2. I don't know why, it's usless, but it contributes to your farm.

Ducks: (see CHICKEN COOP)

Goat:
Van sells a goat in Chapter 2 for-WHAT?!?! 4000g?!?! That's too much for my budget-but if you found a way for money-making, tell me-erm, uh, no, I meant, uh, you...you can afford it, then...heh heh, yeah.

Feeding/Food
Each animal has their own bin, except for chickens & ducks (see CHICKEN COOP). The cow has two holes, instead of one, like the rest. To first get fodder, use your sickle in the pasture and cut the grass. Don't worry, it'll grow back. Then, go inside to the upper-left corner of the room and you should see a ledge. There, you can take out the fodder and place it in the animal's bin.

Pasture
This is where you can let the animals outside when it's not raining or snowing. Use the bell outside by the doorway to get them all outside (use the bell inside to get them all back in). When outside, they eat freely, so you don't have to worry about that.

NOTE: DO NOT LEAVE THE ANIMALS OUTSIDE!!! ALWAYS FEED THEM!!! THEY WILL DIE!!! First they get sick, then you have to buy animal medicine, and if you don't, they'll die. Trust me. It happened to me once (not on purpose!!)