Chickens: Chickens can be bought from Green Ranch for 1500G. You can keep up to six. You must care for chickens by feeding them daily with feed bought from the ranch. Assuming you do so, chickens will lay eggs daily that sell for 50G each. You can reproduce chickens by placing a chicken egg in the incubator. The egg will hatch a few days later. The chicken will remain a chick for about a week, and during that time it won't lay eggs, but you won't have to feed it, either.
Cows: Cows can be bought for 6,000G and can be sold for 5,000G. They're kept in your barn, and you can keep up to eight of them altogether. If you purchase a cow from Green Ranch, it won't be able to produce milk until a season passes. In order to milk it, you must purchase a Milker from Rick's Tool Shop. Make sure to feed it and brush it daily: The better you take care of it, the better quality milk it will produce, and the more money you make. In order to feed it, you'll need to either grow grass on your farm and cut it to make fodder, let your cows graze in the grass, or buy fodder from Green Ranch. If your cow wins the Cow Festival, she will produce Gold Milk, which sells for a whopping 500G per day! If you wish to impregnate a cow, buy a Miracle Potion from Green Ranch and give it to your cow. She'll be pregnant for 21 days before she gives birth. While pregnant, your cow will produce less milk, about a full grade lower than she produced before (If she produced large milk before she was impregnated, she'll produce medium milk).
Sheep: Caring for sheep is very similar to caring for cows. They're kept in the barn along with your cows, and you can keep up to eight. Unlike cows, you can't impregnate sheep, so the only way they can be obtained is through Green Ranch at the price of 4000G. Sheep, like cows, need to be brushed and fed daily. Sheep need to be sheered once a week, using the sheers that can be bought from Rick. Depending on how well you take care of your sheep, the wool will be at varying qualities.