They're easily caught with a live trap and cat food.
Once you have it trapped, what do you plan to do with it? It's almost definitely illegal to transport it and release it, so your option is to kill it or let it go where you caught it which is obviously pointless.
A .22 will kill it easily, but you should avoid shooting it in the head, for several reasons. First, that usually makes them tense up, and release their musk. Second, skunks are one of the most likely carriers of rabies, which is a disease of the central nervous system. Considering the brain is part of that system, and that blowing a hole in it's head will almost definitely result in the distribution of some brain matter, it's not a recommended option.
If you do shoot it, shooting it in the lungs is a better option, because it normally results in the animal relaxing and not releasing its musk. Avoid hitting it in any large bones though.
There are other, quieter, cleaner, methods to dispatch a trapped skunk.
First, simply walk up to it calmly and slowly with an old blanket held up as in front of you (arms spread). Use the blanket as a shield/blind (so the critter doesn't see you), walk up to it, and lay it over the trap. It sounds nuts, but skunks don't just spray at any old thing, and they don't know what a blanket is, let alone feel threatened by it.
At this point, you can actually pick the trap up and carry it if you so desire, and the skunk won't spray.
An easy dispatch option is to run a hose from your car exhaust under the blanket, and run your engine for a little while. Another is to drop the trap into a garbage can full of water (just do it calmly/smoothly; skunks aren't threatened by water, so no spraying). Another is to use a syringe taped on a broomstick loaded with acetate, and inject it into it's lungs.
