This is probably a better question for r/AskAnthropology, since domestication and spread of cattle mostly happened before historical times (except in the new world). But I'll try to provide a brief summary.
Cattle domestication began around 10,000 years ago, independently in two parts of the world: the region around southern Turkey, and the Indian subcontinent. In both cases, the wild species was the auroch, but different types of aurochs that had been reproductively separated for a long time. This resulted in two species of domesticated cattle: Bos taurus in Turkey, and Bos indicus in India. They are commonly referred to as taurine and indicine cattle, respectively. They share a common auroch ancestor about 200,000 years ago, so you can see that there are pretty deep structural differences in the two populations.
Most modern cattle are hybrids, since there are few pure taurine or indicine cattle around anymore. But as expected, European cattle have a much larger taurine component, while Indian cattle have a much larger indicine component.
From the map I linked above, you can sort of see how cattle spread across the world. In the region around India, the indicine species is dominant, meaning they spread from India. In the region around Turkey (including Europe), the taurine species is dominant, indicating a spread from Turkey. In areas settled by Europeans (North America, Australia), taurine cattle are dominant because Europeans took them along. The same is true for China and Japan which don't have much of a tradition of cattle herding, but imported European cattle in recent times.
Cattle herding is quite old in Africa. Generally, it shows an east-west cline going from indicine to taurine, and a north-south cline going the other way, except for South Africa which has more taurine admixture because of the British/Dutch settlement. South America is a different case: although it's part of the new world which had no cattle before 1493 and even though cattle were brought by Europeans, the indocine type heavily dominates across Argentina, Brazil, Chile - the beef producing belt. This is because Indian cattle are hardier, more resistant to drought. They thrive better than European cattle in South America.
This figure shows a principal component analysis plot of about 1,500 cattle genomes sampled across the world. As you can see, the main separation along principal component 1 is between the taurine and indicine species. The dots are color coded by region of origin. Dark orange circles represent indocine cattle, while the blue triangles represent "Southern Europe", which is the closest to taurine cattle that we have today. You can see how taurine cattle split into different regional variations going up and down principal component 2. The reason for the extreme separation of Great Britain (rather than northern Europe which you might expect, being farthest from Turkey in Europe) is because Great Britain is an island, so their cattle populations were more sharply segregated from mainland Europe.
African cattle are midway between the two, indicating a hybrid of taurine and indocine. The separation of African clusters along principal components 1 and 2 basically shows the east-west and north-south clines I mentioned earlier.
This figure shows the spread of taurine cattle from their original domestication sites in southern Turkey and northern Syria (brown region). Bos is cattle (Bos taurus), Sus is pigs (Sus scrofa). This map is based on archaeological evidence of the earliest cattle bones associated with domestication. All dates are BC, so domestication is around 10,000 years old (8000 BC), and by 8,500 years ago, domesticated cattle are in the European part of Turkey, just before their spread to southern Europe.
It's important to keep in mind that cattle are used for both meat and milk, but the use for meat is much older than milk. If you look at maps showing the lactose tolerance sweep across our genomes, you'll find that it's relatively recent. For example, most of Central Europe was lactose intolerant as little as 4,000 years ago, and northern Europe even later. They did have cows, but it was small herds mostly used for meat. Dairying (and breeding cattle specifically to increase milk production) happened much later.
