If you already have the robot animal then all you have to do is buy the livestock through the television. Click on the right tv show in the tv menu... it's Farm World or Animal World or something like that. I can't remember the exact name.

Good luck!

You have to buy the chickens through your t.v. It's the last option you can select (besides cancel). The chickens will be sent down to the barn in your storage area. After you get chickens go back and talk to the farmer and he'll give you what you need to buy cows and sheep and you just buy them the same way you buy the chickens. The cows and chickens are kept in the same barn but the sheep are kept in a seperate barn in the storage area.