Developing And Understanding A Character's Skills

It's no secret that I shelved my fantasy novel for a while because I couldn't get a post-apocalyptic story out of my head.  As I'm getting to know my own characters better though, I start to wonder if it's always so hard to figure out where each person "fits" in the world.

For example, if you're talking about a wasteland: Low population, even lower food supplies, limited or no electricity, desperation. . . Each person needs to have skills to survive and possibly contribute to that new society, don't they?  It would take a lot more than just the average Joe going to his 9-5 to process papers every day.  You'd have to learn something meaningful.