You can frighten a skunk out of a den using bright lights and/or loud noise but be careful — you might cause them to spray.
Don’t seal up a den until you are sure the skunk(s) have left for the evening. Sprinkle a layer of chalk dust, corn starch, or flour about two feet around any opening they use to get in and out of the den. After dark, check for tracks leading out. If you do not see tracks, wait and check again in an hour. Once you are certain the den is empty, cover all entry points immediately. To be safe, reopen the main entrance the next day for one hour after dark to allow any undetected and remaining skunks to exit.
If it is breeding season and a litter of kits is in the den, you should either remove the entire litter or delay eviction until young are active and can be sealed out with their mother. Female skunks will return for their kits. Place the kits under a cardboard box or basket near the original den. She will come back, tip the basket over and rescue them. Make sure all skunks have left the den before permanently closing openings.
If you have doubt that all skunks are gone, you can place a one-way door in one opening that will allow skunks to leave but not re-enter. Before installing the one-way door on the main entry, seal all the other openings with hardware cloth, bricks, or lumber. Bury hardware cloth around the perimeter of any known or potential entrance to a depth of at least twelve inches to keep skunks and other wildlife from digging their way in. Install the one-way door in the main entrance and extend the hardware cloth around that entrance as well. Leave the one-way door in place for three to seven days. One-way doors can be made out of wood or pre-made doors can be purchased from commercial sources.