Before choosing the right method, closely inspect the rules in your area. There are regulations governing the poisoning, hunting, and trapping of wildlife, so before you commit to anything, do your research.

Poisoning: This is the first option for a lot of people, but it’s by far the most problematic. Firstly, and most importantly, it is unnecessarily cruel. Poisoning an animal does not guarantee a quick death, in fact, it essentially promises the opposite.
This presents both an ethical and practical dilemma, in that the raccoon will suffer immensely as it crawls away to die, and you won’t be able to predict where the body will eventually end up. It’s possible that by the time you find the carcass, it will have actually attracted many more animals than you had before.
Poison is indiscriminate, so you’re just as likely to poison harmless animals or even wandering pets, as well as the added possibility of introducing harmful toxins into the food chain, once the raccoon’s body is inevitably targeted by other scavenging carnivores.

Shooting: While it is indeed more direct than poison and does not possess the same far-reaching consequences, the use of a rifle or other firearm to kill pests is heavily restricted. You must check first whether it’s legal to shoot raccoons in your area, and if it is you may need a further permit. Even if you have all the proper credentials and the legal go-ahead, shooting a loose raccoon is difficult due to their small heads and agile nature. If you plan to use a firearm to dispatch a raccoon, consider using it in conjunction with a live trap for an easy and painless kill.

Traps: Traps that are suitable for a raccoon can either be lethal or non-lethal. If you plan to kill nuisance raccoon using a trap, make sure to make it as quick as possible. Lethal traps such as grip traps are a more humane way to kill nuisance raccoon, as they clamp quickly down onto the spine to kill it instantly.
Traps such as this should be favoured over more drawn out methods. Many people choose to use a live trap and then submerge the cage in water to drown the animal, which is just as cruel as poison.