I have a crap-ton of experience with this. I trap or kill about 10-12 skunks/yr.
In most states, you only need to be licensed if you are trapping with a leg-grab trap, or for money.
Go to Tractor Supply, or whatever ag store you have there and get a live trap. Put either some chicken, or some Peanut butter and jam on a piece of bread, and use that as bait. Skunks love both, cat/dog food also works, but not as well.
When you trap the skunk, (and you will). Approach very slowly, holding up an old sheet, or very large, old towel. If the skunk starts to stomp his front paws, back off. Approach from the side, so the skunk can't aim its tail at you. I have ever only had a skunk spray once, after I was able to drape the towel/sheet over the cage, (and that was a rabid skunk).
Once you have the skunk covered, transport in the back of a truck to a safe place, and shoot it, or drown it. You can try to let it go. I have a few times, and they aren't very grateful.
I know a guy who owns a large farm, tons of skunk problems, he sets about 7-8 traps every night spring -fall. He just lets the skunks sit out in the sun, and swears they are always dead by afternoon, so long as daytime temps are in the 80s. He says they never spray that way, but I just don't have the heart to let them die for 4 hrs.
If you shoot it, it will spray. They nearly always do. I've heard, "If you kill it quick, it won't spray." That's BS. I have literally blown a skunk's head off and 10 seconds later.... it sprayed.
If it sprays in the back of your truck, wash it ASAP, that spray will eat paint.
