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Matt_Simpson comments on Macroeconomics, The Lucas Critique, Microfoundations, and Modeling in General - Less Wrong
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If you replace von Mises' intuitions with the particular intuitions neoclassical economics is built from ( to the extent that they differ), then it depends on the particular question you are trying to answer. Market activity is approximated reasonably well by the rationality assumption in a variety of cases. Kahnemann and Tversky's evidence that humans are irrational is certainly strong, but in many cases trying to incorporate this reduces tractability to such an extent that it isn't worth it, or at least we don't know how to incorporate it. A good heuristic is to use rationality for long-run phenomena and when possible, use irrationality for the short run.
Even more so, Gary Becker proved in 1962 that you don't need rationality for many of the basic principles of microeconomics to hold. All you need is for each person to have a maximum budget--a noncontroversial assumption if there ever was one.
Many different kinds of non-utility-maximizing behavior and maximizing behavior across nonstandard preferences (sticky actions, bounded rationality, etc) still produce the key results.
This is true, but it's also worth emphasising that in many cases, we do have reasonably tractable micro models that incorporate irrationality [ETA: I should instead have said nonstandard preferences; not all of these are necessarily irrational], and they do get used. (I'm not suggesting you disagree with this, I just don't want to give casual non-economist readers the impression that the discipline as a whole blithely ignores such things.)
How exactly do you use irrationality?
You don't, you use a decision model that incorporates bias.