Traps work by some combination of crushing, choking, hanging or entangling prey. Some traps work by providing tension when the trap is released. But others like the simple snare work when the prey struggles in the trap. An animal caught in a simple snare will probably be alive when you reach it.
The simple snare works as the name implies -- simply. You create a noose, out of twine or fine wire, and attach it firmly to a sturdy stick driven into the ground. Ideally, the animal will walk right through your snare, catching its head in the noose. As it continues on its way, the noose tightens. This will, of course, panic the animal, and in its struggle, the noose only becomes tighter. To be effective, it's important to place the simple snare on a run that gets regular use.
But there are some problems with the simple snare. You have to decide when you set the trap what type of animal you plan to catch. Clearly, a rabbit-sized noose won't catch a deer. For the best results, the noose should be one and half times the size of your prey's head. The noose must be kept open so the animal can walk into it. But don't use anything that prevents the noose from tightening. A noose made of fine gage wire is a good choice. If you use twine, hold the noose open with blades of grass or small twigs.
Not sure that a simple snare will work? Consider a drag noose.