The following paragraphs were taken from the 2005 International Association of Fish and Wildlife Agencies Trapper Education Manual, which, Indiana adopted as their official student manual in 2006.

Ways to safely, quickly, and humanely kill a furbearing animal

Inexperienced trappers should focus on making selective water sets using submersion techniques or kill-type traps. This avoids the need to kill your catch.

Trappers who make land sets need to be able to safely and humanely kill animals, or release them.

Generally, the best way to kill a trapped furbearer is to shoot it in the head with a .22 rifle.
If the animal has bitten someone, or rabies is suspected, choose a heart shot.

Always shoot skunks in the heart since the brain may harbor rabies virus even if the skunk shows no signs of the disease. Trappers should be graduates of hunter education courses and follow all firearm safety rules on the trapline.

If you are not legally permitted to carry a firearm on the trapline due to age or other restrictions, you will have to use a different method. Strike smaller furbearers such as raccoon, opossum, and fox hard at the base of the skull with a heavy wooden or metal tool to kill or render them unconscious. Placing your foot over the heart and chest area and compressing these organs will lead to death.