The snake usually constricts the person or animal until they die by suffocation, due to an inability to expand the lungs. There have been cases where they eat living creatures, including people, but suffocation is pretty guaranteed once they swallow the head.
When I was growing up in Jakarta, they found two enormous pythons in the culvert right next to the elementary school. They sacrificed a goat to lure them out, then when they were dated they just packed them up and took them to a local safari park. The smaller one was about 21 feet long, while the bigger one was 24 or 25. Just huge.