In the largest cattle raising countries - Australia and the USA, huge free ranging herds were kept. Nowadays, we use yards and crushes for husbandry activities such as drafting and calf marking (castration, etc). Small herds can be pretty tame, but it must have been painstaking to cut calves out of a 1000 head herd with defensive mothers out in the open, keeping track of your progress and stopping them from running back in. Was this the case? Or was there a particular way? Corrals/round yards may hold the manually separated animals, but what might free grazers have done without any facilities?
I've seen here in UK demonstrations by U.S. cowboys of cutting into a herd with a larriot, and very effective it is. So many of the cowboy films show herds being driven at speed for miles, which is far from the truth. WE presumably are talking about domestic breeds rather than buffalo, even if they are roaming in a wild context. The stock would never get any flesh on them if they were constantly being run all the way to the rail-head. So, cattle being quite curious, will not charge away unless the stockman charges at them, and I daresay for branding and castration it would not be too difficult to take out stirks from quite a large free-ranging herd.
The process of collecting and separating free-range cattle in early California was the rodeo (which later gave its name to a sporting event). These were held at specifically suited locations; place names in both Northern and Southern California refer to the practice.
Several Indian cowboys on horseback (often they were the only Indians locally allowed to ride horses), moving faster than the cattle, could force these into a dense, round whorl with the wranglers at the perimeter. They would then extract individual cattle from the rodeo, for branding or slaughter, by lassooing them with a horsehair lariat (reata).
There are a few details in Burcham's "Cattle and range forage in California: 1770-1880". Also see Cleland's "The Cattle on a Thousand Hills".