How can I confirm a skunk inhabitation, and then persuade the stinky squatter to vacate?
You can try using fox urine in the vicinity to repel the skunks. You can buy it in the hunting section of sporting goods stores. As far as determining if there is a skunk there or not, it could be trick. A motion sensor trail camera would definitely work, but is probably not worth the investment if you don't already own one. To avoid future visits from skunks be sure to keep garbage secure, and avoid compost being out in the open.

The humane society website has a nice section on skunk problems also. 

They will not suggest fox urine because the methods of harvesting it don't align with their views, but they mention using kitty litter, which seems like a reasonable option if you have any at your disposal.