Skunk
http://www.havahart.com/how-to-trap-skunks
Skunks become active in March and April as they are looking for mates. You'll need to trap it and close up access to your shed. I don't think Jerry Buckingham removes skunks, but he can probably refer you to someone if you don't want to go the DIY route.
I am not at all confident in trapping and relocating a skunk without getting myself and my car sprayed. I wish I didn't have to think about this, but I think we also have skunks under our deck. 
We have one that lives either underneath our porch or our neighbor's porch (we aren't 100% sure of where it is living). We have young children (1,3, and 6) and don't worry about the skunk. Basically, skunks don't want to interact with your or your children and if left alone they won't bother you. The only time there is an issue is when my sister's dog, who apparently is unable to learn a lesson, tries to catch it and gets sprayed. He's been hit by the skunk three separate times in three years and still hasn't learned, but the smell goes away in a day or so.
ETA: The smell in the yard goes away in a day or two. The smell on the dog lasts about a week or more. Stupid mutt just doesn't learn.
I had a skunk living under my shed. During the daytime I put a small piece of (2x4) wood over the entrance which it could easily move. After just two nights of the skunk having to move the wood he decided to relocate. They are very shy and do not like the idea of anything knowing about or interfering with their lair.
He still sends me postcards.
Be advised that they tend to give birth in late May and June so if you are going to do anything about it you should do it before that.
Our smell has been lingering for weeks outside. Must be because of mating season and repeated sprayings by competing males? I like the sound of Steel's approach. Maybe I'll try that. Now, before baby season.
Thanks everyone! Yes I think taking caring of this before baby season is a must!
I must also add that there was clearly only one entrance for the critter to get under my shed. By the third morning when I saw that the piece of wood had not moved I realized that meant he had not come "home". I then made sure that he or another could not get under there again.
Good luck.
We have two potential entrances I will work on for now.
Are there any substances skunks would not appreciate in their homes? I have heard mice don't like peppermint, so I am wondering whether there is something that would repel skunks in a similar manner.
Ah, another approach to try. HGTV's website says:
"It may seem ironic, but skunks hate certain odors (as if they have room to judge). Citrus, ammonia, mothballs and predator urine (dog, coyote, etc) are three smells that can scare off skunks. If you use mothballs or ammonia-soaked cotton balls, be sure to keep them far away from children."
http://www.hgtvgardens.com/garden-basics/making-a-stink-how-to-keep-skunks-out-of-your-garden?
I am going to try some ammonia, or maybe start with citrus first, as a smell that would not keep me away from my own deck.
Ammonia keeps the raccoons away - I don't know about skunks but I would think it would keep away just about any animal.
mjh said:
Ammonia keeps the raccoons away - I don't know about skunks but I would think it would keep away just about any animal.
According to HGTV, that is sound reasoning.
Regardless of what deterrent smells you may use or not use, I would still recommend putting a little piece of wood over the entrance during the day. If it is still there in the morning it means the skunk has moved residence (since they go out-on-the-town every night).
If the wood has been nudged aside, -you know that he still lives there.
I have a lot of space from the ground to the shed so I don't think the skunk would need to dig to get underneath....
I have spotted two places where the little bugger could get under the deck, so I will try this. One of them is an access door that had been pushed open, which my husband pushed closed and latched a couple of days ago. That leaves one... Which I will block later today.
I think I have a skunk living under my shed. The smell has been around for most of the winter and this past weekend I went by the shed and the smell was quite potent. Anyone have any experience with this? I read that skunks are nocturnal but I have young children. I have a call into Got Wildlife but figured I would ask the group. Thank you