Cows are the best source of animal income. Having four adult cows producing milk create more money then four chickens can produce. Cows are even a better source of income then Sheep.
The cow barn will already be on the farm in the beginning. It is the first barn directly east of the farmhouse. You can buy cows from Chet at the animal shop in the village, but he'll only sell you a cow after you have planted at least 8 bags of grass back behind the cow barn in the pasture area. The grass also must be sprouting and not sitting in seed-form. A cow from Chet costs 5000G. It's a good idea to also purchase the Brush as well. It costs 800G. Chet also has Cow Feed for sale in case you run out of grass. He will have 1 bag for sale and won't have another bag of feed for sale until you use up the one you have.
Remember to check back at the pasture to see if the grass is tall enough to be cut with your sickle. Cut grass equals food for all of your animals, not just your cows. Summer and Winter storms destory random patches of grass, so it's a good idea to replant grass after the last storm in Winter. That way you'll have plent of grass when Spring comes again.
Inside there are four feed-bins for each one of your cows. Every day you need to take food from the bin in the southeast corner of the barn and place it in the feed bins. You don't need to put food in each of the four bins if you only have less then four cows; just in the feed bin that the cow is in front of when you first enter the barn. If you run out of food and have bought Cow Feed from Chet, the bag of feed will be in the southeast corner of the barn.
There is also a feed-bin in the northeast corner for when you have a pregnant cow. The Cow Seed costs 4000G from Chet, and he will only sell it if you have three or less cows. No point in inpregnating a cow when you already have four, right? When you buy the seed and use it on an adult cow, don't forget to put food in the northeast corner bin. The cow will automatically be in the northeast stall area once you leave and then return to the barn. As long as you remember to put food at the pregnant cow's food bin every day, the baby-cow-counter will continue to count down the 30 days until a baby cow is born. You can find out how many days are left by talking to the cow (which you should do anyway) or going into your cow data screen (press SELECT twice) and then picking the selection about your cows. After the 30 days are up, in the morning you get to name the new cow. The color/spot pattern on the new cow are completely random - a black cow can give birth to a brown cow.
In the southwest corner of the barn is the shipping bin. Here is where you will put the milk, cheese, and butter so that you get paid for your hard work. You can buy the Milker from Will for 1800G. Eventually he will have the Cheese Machine and the Butter Machine available to buy, typically after you have four cows that are producing milk. The Cheese and Butter Machines cost 30000G each and are placed in the northwest corner of the barn. To use the two machines, milk a cow using the Milker, then take the milk and toss it onto one of the machines. The machine will chug along a little bit and then spit you back the results. Then just take the finished cheese or butter and throw it in the shipping bin.
If you want, you can take your cows out into the pasture in the back of the barn. To do so you need the Cow Bell, which you get free from Chet when you buy your first cow. To use the bell just go outside in the pasture and ring it. The cows will automatically appear outside. Pregnant cows will not go outside though; just small, medium, and large cows. Don't forget to bring your cows back inside before you go to bed! Leaving the cows outside overnight will result in unhappy cows for 3 days. To return the cows back into the barn, use the Cow Bell inside the barn.
Cows and Sheep both have a Love Level. In the cow's case, the Love Level determines what size milk the cow is going to produce. A cow with 8 or more hearts will produce Large Milk and a cow that has less then that will produce Small Milk. You can see how many hearts a cow has by going into your system notebook (press SELECT) and then press SELECT again to bring up your inventory screen. A cow's data screen will tell you if the cow is happy, what it's name is, how large it is, and how much love it has for you. If you happen to have a pregnant cow, the cow data screen will also tell you how long you have to wait before it gives birth.
If you notice that your cow is unhappy and wont produce milk, feed and brush it for 3 days. If it is still unhappy after 3 days then your cow may be sick. Chet sells Cow Medicine for 1000G each. Use it on the sick cow and the next day it should be better.