Certainly they fear little or nothing in their environment. Therefore, caution should be used in handling them. The heavy, beak-like jaws can sever a broomstick, or a finger, quite readily. Snappers must be handled very carefully. Usually, they can be carried by the tail, and neither the head nor the claws can get you.
Terrapins are easy to handle, since they tend to pull into their shells.
Simply grasp them by the sides. Catching turtles isn't hard at all. The lazy man's way is to use jug lines. A large fish hook is snapped onto a wire leader, and the leader is attached to a plastic jug by a length of line. Chicken livers make a good bait.