Such as? I am probably unable to give you a wholly general prescription for P(X | nuclear war is going to happen) valid for all X; I have even no idea how such a prescription should look like even if infinite computation power was available, if you don't want me to classify all sorts of information and all sorts of hypotheses relevant to a nuclear attack. Of course it would be nice to have some general prescription allowing to mechanically detect what information is relevant, but I think this a problem different from Bayesian updating.
"Apply Bayes' rule anyway" is not a method of reasoning unless we have some way of determining what the numbers are. If we don't have a method for finding the numbers, then we still have work to do before calling Bayes' rule a method of reasoning.
I've been on Less Wrong since its inception, around March 2009. I've read a lot and contributed a lot, and so now I'm more familiar with our jargon, I know of a few more scientific studies, and I might know a couple of useful tricks. Despite all my reading, however, I feel like I'm a far cry from learning rationality. I'm still a wannabe, not an amateur. Less Wrong has tons of information, but I feel like I haven't yet learned the answers to the basic questions of rationality.
I, personally, am a fan of the top-down approach to learning things. Whereas Less Wrong contains tons of useful facts that could, potentially, be put together to answer life's important questions, I really would find it easier if we started with the important questions, and then broke those down into smaller pieces that can be answered more easily.
And so, that's precisely what I'm going to do. Here are, as far as I can tell, the basic questions of rationality—the questions we're actually trying to answer here—along with what answers I've found:
Q: Given a question, how should we go about answering it? A: By gathering evidence effectively, and correctly applying reason and intuition.