At the present time there are just the three types of animal you can get as livestock, the Chicken (creates eggs), the Cow (creates milk), and the Sheep (creates w.ool).
Each of the three types is raised in its own specific enclosures and areas, and those are where you have to go to collect the product that they create.
In the case of Eggs you sell those - after collecting them daily - at the Chicken Icon in town. For Wool you sell it once the pallet is filled, and for cows the milk is stored in tanks and sold.
Bear in mind that animal crops require specific efforts. You must gather the eggs produced by your chickens each day and take them to the market to sell them. You must collect the wool pallets from the sheep farm and sell them to the market. Same deal for cows and milk. Just saying....
Any new animal add ons in the future gettn little bored with three