How does one go about finding work and getting experience in "the field?"
Ryan's suggestion of finding someone to work with is a good one. "Beginning" may not be the right wording, but the spirit is there. Look for people who are at or above your skill level to work with.
One resource you can check is Meetup.com. Look for film/video production groups in your area and get involved with them, that site is pretty good for those sorts of things. You could also look for the nearest 48-hour film festival location and get involved with a group doing that.
That will cover your basic networking with people who are at or near your skill level. Foster and maintain those relationships, you never know what they can lead to.
On the more professional side, you should try to make contact with established company's/individuals that are in your area. I got my first internship at a professional studio by walking into every recording studio in Boston I could find, resume in hand. I worked there during my days off from work, and it made a big difference. With that being said though, don't allow your ego to get in the way.
If you can get a job photocopying or answering phones somewhere you might like to work as an audio tech, take it. Let them know you're interested in more, make friends with the mixers/editors, and ask to sit in on sessions that occur outside of your normal working hours. If they let you do it, you should be cheerful, polite, dedicated and stay out of the way/keep your mouth shut. Let your work ethic speak for itself. Remember the three big quesitons: "Do I need to say this now?" "Do I need to say this now?" and "Do I need to say this now?" [hint: if the answer to all three is, "yes," then you can think about saying it.]
I'd like to say there is more to it, but there really isn't...other than persistence and one thing that none of us have control over, luck. There's a possibility that you might be able to do some of this long distance/telecommute. Who knows?! The internet is a wacky place now-a-days.
EDIT: I neglected to mention looking into other local media companies that may not be directly in the filed you're looking at at the moment...which is funny considering I used to do dialogue editing for a company that produced web based compliance and ethics training courses. lol
I asked this same question not too long ago.
Might be useful to ya. Cheers!