"...I picture it as something you would have to be taught, not just learn on your own."
Bam, Since I didn't want to spend a bunch of $$ on classes, I learned it on my own by reading a lot, watching you tube videos, and perusing various carving sites on line. I started out doing a little relief carving and finally delved into carving "in the round". My wife and I enjoy bird watching, so it was a natural for me to want to carve birds. My advice would be to concentrate your carving on subjects you really enjoy, whether it is birds, animals, caricatures, people, or whatever. The more interested you are in the subject, the more likely you are to want to perfect the carving.
If you want to take a class, I would highly recommend getting in touch with a member here...Stave. He is located in Asheville and is a true artist. Take a look at his work in the photo gallery. I wish I could come close to the work he does. I'm not sure if he is doing any classes, but I have heard very positive feedback from other members who have worked with him.