To be fair, there are a lot of resources I've seen on various game development websites; the forums at gamedev.net come to mind, and there is a list of other websites available here. Generally speaking, you either put together a resume and portfolio, and let people come to you, or you go asking around at specific companies, which is riskier and brings on higher expectations, but shows more initiative and drive.
As far as professional-quality audio production being only in the domain of "big budget game studios", this is only true on the notion that independent game studios simply cannot afford the audio production costs for games that are statistically far less likely to be commercially viable. If a studio has the resources and the will, they'll spend whatever they can afford on audio, but since most independent studios work on shoestring budgets either from previous successes, fundraisers, or personal contributions, many won't push for more expensive sound production.
If you're looking to prove your mettle with a first-try game project, and you're willing to offer discounts or special agreements with independent studios or game projects, then you'll probably see a few more buyers come your way from mid- to low-budget territory. But like everything in game development, deciding whether or not to hire a quality sound production team is a calculated risk, with the goal being to improve the overall player experience through better sound. For an audiovisual-experience game like Journey, this plays a major role in driving the point of the game; for smaller titles, sound effects and music may be an afterthought, or done with whatever resources are available. Just keep in mind that many developers just want good-quality audio on the cheap... though of course, the smattering of indie games of the last few years with compelling music and good-quality audio is leading to some significant changes in this area.
Just keep in mind that the most important thing is to have a strong, diverse portfolio of prior work; no one will hire an audio engineer with top-of-the-line equipment and no clue how to use any of it. (In fact, if I were in such a position, I'd rather hire a kid off the street if he hacked a Game Boy to remake new audio for Super Mario Bros., just because of his knowledge and drive.) As far as portfolio pieces go, any work that you have with relevance to the game, the studio, the genre, or just for game-related audio projects in general (fan-made soundtracks, custom compositions of game music, VO projects, sound effects, etc) will probably be best.