On your farmland you will have two barns; one holds your chickens and the other is shared with your cows and sheep. The chicken shed has room for 4 birds, and the animal barn can hold up to 8 cows and sheep. If you want to own more animals, you'll need to upgrade your barns.
To upgrade, talk to Gotz the carpenter. He will upgrade your chicken shed for 5000 G and 420 pieces of Lumber. The cost for the animal barn is 6800 G and 500 pieces of Lumber. Gotz will spend 3 days working on your upgrades.
After your barns have been upgraded, you can buy the Makers that allow you to create Cheese, Yarn, and Mayonnaise. You'll earn more money if you convert your produce into their upgraded forms. You'll need the Makers if you plan on cooking any recipes like Pizza and Fondu, or participating in the Stocking Festival every Winter.
The new animal barn will have two special stalls you can use for housing your pregnant cows and sheep. You also have room to hold 16 animals. You can use any combinations of cows and sheep you want. You could have 15 cows and 1 sheep if you felt like it!