These are learnt best in full drama (not just acting) lessons, with daily, weekly or monthly performances and at least some devising left up to the students, letting them work it out together with decreasing guidance. I've taken these types of drama lessons for four years, and found them very useful for the above. I took formal acting lessons (where the teacher made all the decisions, gave all the feedback) and quit after three months.
A good way of teaching it can be to demonstrate concepts through lecturing and requiring daily performances for a week or two (have everyone perform at the end of the lesson) and then letting everyone get into groups with scripts and design their performance for a month or week from then, with whatever restrictions, advice, resources you decide. Organizing rehearsals is another good and transferable skill.
These might not go too well in short hour or such lessons, though - but getting people to create a short minute or so performance on a topic/style with a few people in their off-time, and present in class, would do as well and leave more time for 'teaching'. People can also laugh and joke and, I've found, do better work in their own rehearsals then in a class format with other groups all around them.
Recent brainstorming sessions at SIAI (with participants including Anna, Carl, Jasen, Divia, Will, Amy Willey, and Andrew Critch) have started to produce lists of rationality skills that we could potentially try to teach (at Rationality Boot Camp, at Less Wrong meetups, or similar venues). We've also been trying to break those skills down to the 5-second level (step 2) and come up with ideas for exercises that might teach them (step 3) although we haven't actually composed those exercises yet (step 4, where the actual work takes place).
The bulk of this post will mainly go into the comments, which I'll try to keep to the following format: A top-level comment is a major or minor skill to teach; upvote this comment if you think this skill should get priority in teaching. Sub-level comments describe 5-second subskills that go into this skill, and then third-level comments are ideas for exercises which could potentially train that 5-second skill. If anyone actually went to the work of composing a specific exercise people could run through, that would go to the fourth-level of commenting, I guess. For some major practicable arts with a known standard learning format like "Improv" or "Acting", I'll put the exercise at the top and guesses at which skills it might teach below. (And any plain old replies can go at any level.)
I probably won't be able to get to all of what we brainstormed today, so here's a PNG of the Freemind map that I generated during our session.