Don't startle the baby skunk. If you find yourself near it, move away from it as slowly and cautiously as possible. If someone's with you, use only soothing, soft tones when speaking to one another.
Seal off the area where the skunk lives, keeping only one entrance open for it to get out and feed. Pour a layer of flour on the floor of the entrance and use it to monitor footprints. When you find footprints indicating that the skunk has gone out but not returned, seal off the rest of the area.
Purchase a humane trap for the skunk that captures it without hurting it. You can lure the skunk in with peanut butter on bread. Unlike humane traps, a trap that injures the skunk is more likely to put it on the defensive and cause it to spray on your property. Cover the trap with a large blanket to avoid frightening the skunk and getting sprayed.
Contact a wildlife professional, even if you've trapped the skunk yourself, because a professional will know where you can take it. These professionals are often employed by wildlife preserves and state parks. Your local animal shelter may also be able to help you find one.
Show the wildlife professional where the baby skunk is living if you haven't been able to trap it. Stay as far away from the skunk as you possibly can. (Typical areas for baby skunks to be found include patios, porches and crawlspaces.) Continue to use slow, cautious movements and to talk in a quiet tone if the skunk is nearby. The professional will handle the rest.