When cowboys rope a cow with the intention of bringing it down to the ground it normally requires two cowboys although I’ve seen it done with one. The first cowboy is designated as the “header” and he puts his rope around the cows head and tightens it around the neck. This basically controls the area that the cow can move in (a circle around the cowboy’s horse) although in practice the header often moves the cow slowly forward in the direction he wants to give the heeler a better shot.
The “heeler” then throws a loop around both the cows back feet and tightens it. You do that by putting a properly shaped and timed loop on the ground in front of the back feet (I’m over simplifying it) and when the cow moves forward it steps into the loop, which the cowboy then tightens. Sometimes you only get one foot.
When the two cowboys move their horses backwards the roped cow becomes gently stretched between them and can’t move. It’s possible to actually put the cow down on its side by controlling the angle of the ropes but most of the time a groundsman approaches the cow and pulls it down to the ground on its side. Or one of the cowboys gets off his horse, which has been trained to keep tension on the rope, and performs the groundsman role.