A few I do regularly;
Odds calibration. Make predictions, with odds, about things. A number of people do this on a yearly basis (https://www.vox.com/future-perfect/2019/1/15/18182069/2019-predictions-forecast-democratic-nominee-brexit) but you can do it on a much shorter range as well, estimating how long a chore will take, which people will arrive to a dinner first, or how much a company's stock price will move after some announcement. "My next meeting today will not wind up canceled, 80% confidence." Write these down somewhere accessible (though probably private) and record the accuracy. The goal is for the things you say will happen with 80% confidence to happen eight times out of ten.
Be wrong. State aloud and write down some fact about the world that you think is true, think of an authority you would trust (Wikipedia is a decent starting point here) and then look it up. "The population of Houston Texas is between one and two million." If you are right, bask in the warm glow. If you are wrong, admit aloud that you are wrong, and what the right answer is. The goal is to get used to saying this when it is correct to say. (Speaking of which- I was wrong, the population of Houston is over two million.)
Follow curiosity. I'm not confident that "keep googling questions and clicking links in Wikipedia until you feel the confusion disappear" is especially efficient, but learning what "wait a minute, I'm still confused on how this actually works" feels like is easier to me when there's no pressure to nod and move along with the class. Notice the feeling of confusion, and what makes it disappear. (I'm curious what happened with Houston's growth spike from 1999 to 2000- Montpelier Vermont and Lincoln Nebraska show similar jumps that year, but not Albany New York or Orlando Florida- but it looks like my meeting was only delayed and not canceled, so I'll have to figure that out later.)
Out of curiosity, is there any tool to facilitate personal predictions? When I've tried to do this in the past (using a Google Sheet) I tend to forget to score my predictions. I did some basic searching for a short-term prediction tracker (ideally something that would let you mark the outcome of a prediction and then calculate your calibration over time) and couldn't find anything. This seems like the sort of thing that could be languishing in someone's Github.
Alternatively, if this tool doesn't already exist, should it?
This may seem stupid, but I didn't even think about doing odds calibration on such a small scale. That's a great idea. Making a pinned Google Keep note now.
Probabilistic forecasting (for evaluative thinking) and Fermi estimates (for generative thinking).
A thing I frequently do is literally just take an object and start observing things about it. Notice what I notice. Notice what conclusions I generate, what assumptions they're built off of, and what parts of my brain they come from. Notice interactions with other mental models, notice what hypotheses are testable.
Also try some kind of precision physical art, because the brain's primary job is and always will be moving your body. There's a lot of prior art in how to move your body better, and I would be surprised if fine-tuning that didn't translate at least a little bit into increased intellectual fitness.
(I should take my own advice, meh.)
I think trying to predict human behavior, and developing ways to do it best, is a great exercise, and one that can also have immediate benefits (being better at predicting what people will do makes your social skills better).
This can also be taken as a full project of rationality, doing scholarship (science of people), using math and probability (maybe even inventing your own algorithms), gathering, organizing, and analyzing data (like personality types of people you know and what can they tell you about them)...
In Martial Arts, we have 'forms' that allow us to practice our skills when not with a partner or in adversity. In Rationality, I imagine that this would take the form of "brain teasers", but specifically regarding decision theory, overcoming biases, and calculating probabilities.
What are some things one can do to practice Applied Rationality? These can take the form of thought experiments, websites, apps, pen-and-paper tools, etc.
These would ideally range from "easy to do within a couple minutes" to "you need to dedicate a day to this".