I have several rental properties, and one in particular seems to get a skunk living underneath it every year. I set out a live trap and will sometimes catch the skunk, sometimes catch the tenants cat. I've caught half a dozen skunks the last few years and have learned the best way to move them.
Susan pretty much has it right, with one exception, IMHO. Don't use clear plastic. Use dark plastic or cloth that the skunk can't see through. It keeps them calmer if they can't see you. I happened to have a white plastic covered table cloth for an outdoor patio table. It is round and has a hole in the middle (for a table umbrella). The hole is perfect because it goes over the handle and makes it easy to carry.
I relocate the skunks to my property, 33 acres in a rural area. I have no problem with the skunks. They mosey on never to be a bother. I would NEVER relocate a feral cat out here. Feral cats are nothing but destructive to native wildlife. They are still an occasional problem, but usually solved with a .22. When I lived in a more urban area, a carefully placed CB Long was the bomb. It might seem cruel to whack the cats, but it's more cruel to the native songbirds, lizards, frogs, and everything else they're killing out.
lukus