You can breed three types of animals: pigs, cows and sheep. In order to buy animals you must drive with an animal transportation trailer to a shop. Here, you can also sell your animals if you have too much of them. If you don't feed them you won't get any goods. However, animals won't die. Your farm should be optimized in a such way that you can give your animals whatever they need in time. First, try to choose only one type of animals. You deliver food and animals to the same place in your farm (you can see an icon of a given animal, you only have to stop your trailer in the right spot).
They are the easiest to breed and are recommended as your first animals. An optimal starting number of pigs is 30 heads. Your starting fields allows you to provide them food without having any pauses in production. You earn money by selling pigs that are generated every 1:30-2:00 minutes. Each subsequent pig reduces this time by 2 seconds. When you give your pigs straw made from wheat they provide you with fertilizer but this has no impact on production. However, you have to feed them with rapeseed and corn - if you don't give them one of the two types of food they will lower their reproduction by a half.
Cows are rather hard to breed. They can, after some time, replace pigs if you buy a big field of grass and a lot of cows. They also generate fertilizer if you bring them straw which is useful for your next crops. In order to feed them you only need grass or hay - giving them both has no impact on their performance. The default meadow can feed about 15 cows. They also give you milk 1/second if you have 15 heads. Their reproduction time is about thirty minutes (when you have 15 cows) but this time is reduced with each new head by about 3 minutes.
Just like cows, sheep also need grass or hay (their performance is the same whether you give them one type of food or both), however, they don't generate fertilizer. They provide you with wool which is the most expensive resource in the game. However, the process of getting it is very slow and because of that you must buy a lot of sheep and a big field. The starting meadow combined with hay or grass allows you to breed about 20 sheep. Their reproduction time is about 22 minutes when you have 20 heads (each subsequent sheep shortens this time by 4 seconds). The same amount of sheep (20 heads) allows you to produce 1 wool/second.