I recently got a request for advice on how to break into an ARG career; this is my answer, and I thought I'd take the liberty of sharing it here in case anyone else would find it helpful or interesting.
Sooo, you want to break into ARGs. Sadly, it's not a lot different from any other business; lots of it boils down to diligent networking and proving you can do the work, and do it well. Here are some specifics, though:
First, this is a great question to pose on the ARG development community the IGDA maintains. You can subscribe to the mailing list here. There are a lot of great minds in the current ARG world there, and these are the people who will know what to tell you, and who may even be looking to hire you. (Please, though, don't go asking for a job on the list as that's not what it's for). In general, becoming involved in the development community can only help you to raise your profile and find the position you're looking for.
So far, there seem to be about three primary routes to becoming a professional ARG developer. First, many high-profile players have made a transition into a career; my own company has hired a number of players like that by now. This is probably the least-reliable way in, though. :)
In the more-probable realm, if you're trying to get a job with an existing ARG studio, the most important thing would be to demonstrate your abilities somehow. The simplest way: Make an ARG, build a portfolio. If you're making it purely for demo purposes, you don't need to spend lots of money on it, and it doesn't have to run for very long; just use your storytelling flair and any clever tech innovations you might have up your sleeve to make something you're proud of.
Quality would be key, here; for example, if you want to write, try to demonstrate a couple of distinct styles and voices. If you want to write code, make sure you're debugging thoroughly, providing for draconian security, creating a usable interface, etc. If your aim is to be a producer and/or game designer, pay attention to the overall arc of what you're doing to make sure it fits together as one cohesive piece rather than, say, a loose string of unconnected puzzle games.
Lots of ARG studios do contract out some work to designers, writers, programmers, or what have you. Once you've got a portfolio that demonstrates what you can do, try to establish ties to one or more ARG studios in a freelance capacity. This will build your overall street cred and improve your chances of getting a full-time gig over the long haul.
The third way to become an ARG developer is to start up your own studio. A lot of that has been going around the last few years! If that's what's right for you, then you should be looking up advice about getting venture capital and marketing a new company to a potential first client, and that's not something I'll be able to help you with very much.
Best of luck!