How do cows make milk?

The process starts in the rumen. The grass in the rumen is broken down into molecules and tiny pieces through the process of fermentation by microflora in the rumen and rumen contractions which help mix all the liquid and solid matter together. The process of fermentation helps break through the tough plant matter like cellulose, fibre, lignin and hemicellulose and enable nutrient extraction. These nutrients include carbohydrates, lipids, proteins, vitamins and minerals, which are absorbed through not only the rumen wall, but also through the omasum, abomasum and small intestine (primarily the small intestine). Capillaries which link to blood vessels transport these nutrients to different parts of the body, including the udder of a cow.

Inside the udder there are many different vessels and cisterns and "holding units" where milk is stored, as well as many tiny alveloi. In these alveoli is where milk cells are located, which are linked to capillaries and blood vessels that have carried all this nutrient-rich blood from the digestive tract of the cow to the udder. There, the nutrients and other goodies are deposited in the milk cells to be combined into the formation of milk. Milk cells also create other molecules and sugars like casein and lactose. This milk is drained into the alveoli which, after filling up, drain into vessels into various cisterns which all drain into larger cisterns and so on until all the milk is collected into the Glans Cistern, the largest compartment where milk is collected. Once this area fills up (making the udder, on the outside, appear large and swollen), milk is let down by the hormone Oxytocin into the teat canal, which is excreted with the help of the suckling action of a calf, a milker, or by a milking machine.

Answer 2: The process starts in the rumen. The feedstuffs (this varies between beef and diary producing animals) is broken down into molecules and tiny pieces through the process of fermentation. The rumen, omasum, abomasum and reticulum are equipped with bacteria and protozoa that are able to absorb the necessary nutrients that aid in milk production. These nutrients include carbohydrates, lipids, proteins, vitamins and minerals, which are absorbed primarily by the small intestine. Capillaries which link to blood vessels transport these nutrients to different parts of the body, including the developing mammary glands.

The rest of milk production occurs in the mammary gland (also known as an exocrine gland), this gland produces the external secretion of milk transportation through a series of milk veins. The secretory tissue of the mammary gland is composed of millions of alveoli (grape like structures). Each of the alveolus has its own separate blood supply from which milk constituents are obtained by the epithelial cells often referred to as "milk cells." These milk cells are linked to capillaries and blood vessels that have carried all this nutrient-rich blood from the digestive tract of the cow to the udder.

These alveoli will take nutrients from the bloodstream, these structures will then add fat, protein, casein and lactose (a type of sugar) to produce milk. Milk will then collect in the alveolus lumen and, during milk let down (initiated by the hormone Oxytocin), will travel through ducts into a larger area called the Gland Cistern. Once this area fills up (making the udder, on the outside, appear large and full), milk will then continue to travel into the teat cistern and through the teat canal to the outside of the teat. Milk will either be excreted through a machine (the milking system in dairy production), by hand, or by the calf suckling. However, if the cow is a high producer she will often leak milk as she enters the parlour (as oxytocin is already allowing milk to drop into the teat). Beef cattle can leak milk if the calf does not suckle often enough.
Cows produce milk just like any other animal, the nutrition and vitamins from the food the cow eats partly goes into producing milk. The quality and quantity of milk that a cow produces depends on what you feed your cow.