The first challenge is answering the implicit "Why should I care about rationality?" question in a compelling way.
My suggestion is to decide what your answer is for that session, drop the "rationality" label, and talk about that instead. For example, if you're going to talk about the benefits of rationality for making decisions under uncertainty, then your topic is actually "Making decisions under uncertainty."
You may end up with multiple rationality talks... this isn't a bad thing.
Choose concrete examples wherever possible to make your point. Generalizing from a few concrete examples is fine, but starting from the general case can cause trouble. Make your examples either realistic or funny (or both!).
Tie endorsed behaviors to concrete results: "doing X makes Y more likely."
Don't try to cram in too much. Make one primary point, make it well. Have a couple of secondary points in your back pocket if your audience moves a lot faster than you expected, but don't expect to get to them.
Operationalize: give people things they can do now -- either right then, or right after the meeting -- that relate to the point your talk.
I have an idea-outline for a very public-friendly lecture on "why should I care about rationality," and sooner or later I'm going to make a power-point of this and hopefully present it.
Main point: probability calculations will help you make better life decisions.
In the movies, maybe the Chinese ...
I recently discovered that in my home town (Norwich, England) there is currently running a series of "Café Conversations" in which some faculty members of the university that I work at are giving talks/hosting discussions on various topics. The meetings take place in a café that I know, which has room for about 20 people, and are open to the general public. Titles of some of the meetings already arranged are "What is infinity?", "Increasing happiness, decreasing consumption", "Bioplastics: wasteproduct or gold mine?", one on the nature of boredom (really about how old, retired people find things to do), and several on environmental topics. I have not been to any of them -- in fact, only the first of them has happened so far.
The obvious thing for me to do is to volunteer something on rationality, but quite apart from whether I would be able to do that at all (not being the friendly and outgoing, charismatic sort suitable for leading such a meeting), a problem that I foresee is this: these meetings are intended for the general public. This is nothing like a LessWrong meetup, or a Singularity conference, or delivering a lecture which, while nominally open to the general public is not actually intended for them.
Has anyone here had experience of communicating about rationality, one-to-one or one-to-a-small-roomful, with the general public? How do you approach the matter, and how far can you expect to get?
Norfolk, by the way, has given the world the expression "Normal for Norfolk". Go on, Google it.