Better to start concrete: What goals do you have?
If you have simple and well-understood goals, in a domain that has clear rules or which your ancestral environment would reasonably have prepared you for.. you probably don't particularly need "rationality". (ref) Just go out into the world and see, feel, do. Seek ordinary wisdom through experience and listen to your instincts. Anything else will distract you, not help you
I say this seriously: don't try to do things "rationally" just for the sake of being rational. You will kriff up important parts of your functioning while lacking the internal compass necessary to correct the course.
Got it? Good.
Now, to brainstorm the areas you may want to use rationality-flavored thinking on: What do you have trouble predicting? Where is average not good enough? Where do you contradict yourself? What conditions are your plans and strategies fragile to? Where do other people have trouble predicting you? (or predict you too well?)
Look into these. Consider how you can best find out what's actually true.
And then? I suggest journaling.
Boring advice, everybody says it. But it's true. Think out your thoughts in detail. Reflect on the happenings of the day and whether you endorse the decisions you made. Collect questions and ideas to check up on. Track the progress on your goals. Record your intentions and predictions so you can't lie about them to yourself later.
I recommend Zettelkasten or Bullet Journal for an organizing methodology, and Roam/Logseq for keeping a digital notebook, but it also works fine if you just write. Alternately, keep an audio recorder in your pocket.
And if you still really want little rationality modules to practice specific skills or solve particular problems, go to clearerthinking.org.
What works for you to cultivate rational thinking, if you are not doing rationality exercises?