Last updated Apr 02 '12 at 09:40
engineeer87 is spot on. Though I've since moved on, I used to work in music production/engineering (incl. a stint in a Nashville studio). Everyone I knew in the industry (myself included) got their start through a personal acquaintance or an apprenticeship.
I got my first job by making personal visits to all the major studios. I just stopped by and asked if I could work for free. Though most said no, I eventually found one that said yes. After a lot of hard work, they eventually started paying me.
Apprentices/interns work for little to no pay because it's understood that they will receive some form of education during the course of their work. Good engineers will go out of their way to teach you things during the course of your work. Make no mistake, you'll also do a lot of mundane, seemingly mindless tasks.
Pay particular attention to smaller studios, as you'll get more responsibility faster.
As your chops improve throughout the course of your internship/apprenticeship, you'll start to pick up paying gigs. Perhaps a live show here, an extra studio session there, etc. If everything works out and your network of clients expands, you'll eventually find that you're making enough money to eat more than Ramen. There are few salaried people in music - most live check to check.
Best of luck, I hope it works out for you.