To trap a skunk, you have to know its location. Pay attention to where you can see it, or where grass and weeds are being eaten. Alternatively, follow the smell.
Once you find the location, place the body trap somewhere where the skunk is likely to cross its path. Optionally, use bait such as wet cat food. Depending on preference, use a kill trap or a non-kill trap. If you use a non-kill trap, you may have to relocate the skunk, which can be illegal, or take the skunk somewhere where they can euthanize it.
Check the traps every day. The type of trap used dictates how you remove the skunk. If you used a kill trap, then you need to dispose of the body in the garbage. If you used a non-kill trap, then throw a blanket over the trap carefully not to get sprayed, then take the skunk to an approved location or to a local place that can euthanize it.