I'm a law student. I actually use pretty much the same mental toolkit as a gamer that I do for my classes (Yes, I am an honest-to-god rules lawyer, if you want to take it that way.) I was sort of surprised by the specific-beats-general canon they put up front, if only because it was so obvious to me, something I already knew deep into my bones, that it was strange to see made explicit. It'd be like if they called out "Hey. These rules are written in English. Attempting to play the game by reading them in another language will not work as well." Just an observation.
But, anyway, the following describes my general procedure:
1. Everyone with an interest in the matter can make a short statement of their argument for their interpretation.
2. We start out with the plain meaning of the text.
3. The text will not be construed, however, in such a way as to abrogate the clear intent of the drafters, or lead to an obviously inconsistent or game-breaking result. Always construe in favor of balance and consistency.
4. Where all that fails or is evenly balanced, construe in favor of the result that seems to be the most fun, which usually means reasonably construing things in the PCs favor.
5. This process should move along quickly - there's no point to spending more than a minute or two arguing about syntax.
6. Rule 5 may be ignored if a character's life is on the line. If someone is about to be gakked depending on a matter of interpretation, then the matter will receive a much more thorough exploration.
7. The GM makes the final call, and sticks to it.
8. The GM's call can be abrogated by official errata or WotC clarifications, or clever arguments from message boards that are as a matter of procedure brought up OUTSIDE NORMAL GAME TIME.
9. If something is a real problem for my table, discuss and make a house rule to cover that case.