Note: this post is no longer endorsed by the author, for reasons partially described here.
In the spirit of radioing back to describe a path:
The truly absurd thing about dreams lies not with their content, but with the fact that we believe them. Perfectly outrageous and impossible things can occur in dreams without the slightest hesitance to accept them on the part of the dreamer. I have often dreamed myself into bizarre situations that come complete with constructed memories explaining how they secretly make sense!
However, sometimes we break free from these illusions and become aware of the fact that we are dreaming. This is known as lucid dreaming and can be an extremely pleasant experience. Unfortunately, relatively few people experience lucid dreams "naturally;" fortunately, lucid dreaming is also a skill, and like any other skill it can be trained.
While this is all very interesting, you may be wondering what it has to do with rationality. Simply put, I have found lucid dreaming perhaps the best training currently available when it comes to increasing general rationality skills. It is one thing to notice when you are confused by ordinary misunderstandings or tricks; it is another to notice while your own brain is actively constructing memories and environments to fool you!
I've been involved in lucid dreaming for about eight years now and teaching lucid dreaming for two, so I'm pretty familiar with it on a non-surface level. I've also been explicitly looking into the prospect of using lucid dreaming for rationality training purposes since 2010, and I'm fairly confident that it will prove useful for at least some people here.
If you can get yourself to the point where you can consistently induce lucid dreaming by noticing the inconsistencies and absurdities of your dream state, I predict that you will become a much stronger rationalist in the process. If my prediction is correct, lucid dreaming allows you to hone rationality skills while also having fun, and best of all permits you to do this in your sleep!
If this sounds appealing to you, perhaps the most concise and efficient resource for learning lucid dreaming is the book Lucid Dreaming, by Dr. Stephen LaBerge. However, this is a book and costs money. If you're not into that, a somewhat less efficient but much more comprehensive view of lucid dreaming can be found on the website dreamviews.com. I further recommend that anyone interested in this check out the Facebook group Rational Dreamers. Recently founded by LW user BrienneStrohl, this group provides an opportunity to discuss lucid dreaming and related matters in an environment free from some of the mysticism and confusion that otherwise surrounds this issue.
All in all, it seems that lucid dreaming may offer a method of training your rationality in a way that is fun, interesting, and takes essentially none of your waking hours. Thus, if you are interested in increasing your general rationality, I strongly recommend investigating lucid dreaming. To be frank, my main concern about lucid dreaming as a rationality practice is simply that it seems too good to be true.
 Note that this is only one of many ways of inducing lucid dreaming. However, most other techniques that I have tried are not necessarily useful forms of rationality practice, effective as they might be.
 And, to be honest, "fun" is an understatement.