Snares are a great way to take animals from the size of a muskrat or mink, on up... Check the legality of what you can and cannot snare. In Wyoming we can snare furbearers and predators, but not game animals. I'd initially recommend commercial snares. They are inexpensive and built to the size of animal you are targeting. They can be set to dispatch or kill the animal or to restrain them alive. Again, know what is legal in your state. They have locks, and some have springs that help them dispatch more quickly. You can also use entanglement to get them to lock down and dispatch more quickly.
Go to the
http://snareshop.com for supplies and some great tips.
http://Snaremantalk.com is also a great snaring/trapping forum that will shorten the learning curve.