How can one train philosophical skill?

Bit of a side point: One thing I got from spending a lot of time in the philosophy department was an appreciation for just how differently many philosophers think compared to how I tend to think. I spent a substantial fraction of my time in college trying to get at the roots of those differences - what exactly are the differences, what are the cruxes of the disagreements, and is there any way to show that one perspective is better than another? (And before anyone asks - nope, I still don't have good answers to any of those.)

It opened my eyes to the existence of entirely different ways of thinking, even if I still have a hard time wrapping my brain around them.

As I said, I still don't have a great way to even describe the differences very well. But I will at least say that if the kind of Bayesian and/or reductionist thinking that people tend to promote on LessWrong seems essentially right to you and (once you see it) almost common sense, then you should consider spending time talking to traditional non-Bayesian analytic philosophers and try to understand why their arguments feel compelling to them. Or maybe just read a bunch of articles on the Stanford Encyclopedia of Philosophy that describe non-reductionist, non-Bayesian approaches to metaphysics or epistemology. Maybe the discussions there will seem perfectly reasonable to you, but maybe you will discover that there are really smart people who think in fundamentally different ways than you do. I think just the realization of that seems useful.

A friend of mine once suggested a stand-up-comedy type model for philosophy ("stand-up philosophy"). I think this could have some good dynamics. Imagine philosophers competing to blow the minds of the audience and judges.

One thing that served me well, I think, was ambition. Even before I went to college, when I was first falling in love with philosophy, my goal was to solve it. I wanted my worldview to make sense, dammit, and not be full of contradictions and incoherencies and "we don't ask that question" moments. Most of the philosophers regarded as great (Leibniz, Russell, Lewis, etc.) were grand systematizers who attempted to have an answer to everything, and were not satisfied with paradoxes/contradictions/incoherencies/articles-of-faith anywhere. Alas, no one so far has been able to succeed at this ambition, but nevertheless I think I learned so much more, and came to beliefs that are so much better, because of it.

Why? Well, one reason (though probably not the only reason) is that it helped me prioritize. It helped me move on from interesting-but-not-that-important puzzles and go for the Big Questions. And go straight for the throat instead of lollygagging.

The experience of trying to construct a coherent, non-contradictory complete worldview, only to encounter some new problem or puzzle that brings it crashing down, repeatedly is perhaps analogous to the experience of trying to construct a hypothesis about how celestial bodies move, or how optics works, or something, that can accurately predict all the data from all your experiments.

For deliberate practice you need feedback that tells you whether or not you are right with what you are doing. The traditional way for that is essay writing with a teacher afterwards giving you critical feedback about what you wrote. 

Besides written communication, oral communication can work as well if you are doing it together with skilled people. 

I think one of the main problem with philosophy is that it's too detached from practical concerns. If you want to understand the nature of knowledge and how it's aquired you should be able to have practical answer to questions such as how our society should go about deciding whether we know that a particular drug works or doesn't. 

Yes, the question is messy but that's the nature of reality. 

The lazy answer is probably “whatever it is that philosophy grad students do.” I honestly think this might be a good question for a zoom call with a bunch of PhD philosophy students.

I often feel like a lot of problems would be solved if we could just make working through Li and Vitanyi a requirement for aspiring philosophers.

There are two things similar to a "philosophy coach" I can imagine:

One would be if someone has thought deeply about something, and you've only thought briefly, you could try to express yourself to them and then they could help you quickly learn what avenues of thought are more promising than others, and what path they took to reach where they are.

Another is someone better at philosophy writing than you helping you edit your drafts.

Current professional philosophers seem to be generally too confident about their ideas/positions, and lack sufficient appreciation of how big idea/argument space is and how little of it we've explored. I'm not sure if this is a problem with humans, or a problem with how philosophers are trained and/or selected. We should at least make a concerted effort to rule out the latter.

One concrete suggestion is instead of measuring progress (and competing for status, etc.) by how many open problems have been closed (which doesn't work because we can't be very sure whether any proposed solution is actually correct), we should measure it by how many previously unsuspected problems have been opened, how many previously unknown considerations have been pointed out, etc. This is already true to some extent, but to have high status, philosophers still seem expected to act as if they've solved some important open problems in their field, i.e., to have firm positions and to confidently defend them.

(I'm not sure this is the kind of answer you're looking for, but I've been thinking this for a while and this seems a good chance to write it down.)

I would suggest time thinking about mathematical paradoxes. One advantage of these compared to many philosophical questions is that it is easier to engage in these question from the desire to know the truth, rather than the desire for things to work out a particular way.

Another advantage of exploring paradoxes is that often when you make a mistake, there will be a mathematical proof that you are wrong.

Another suggestion I would make would be to pick the area of philosophy in which you currently feel you can make the most progress on and to leave areas in which you feel more uncertain until later.

I've gained a lot of benefit from writing down my ideas. Often arguments that seem waterproof in your head will turn out to have additional assumptions once written down. Often if I come back a few months later, I can see areas where my argument isn't as strong as it could have been.

I can also see benefits of writing steelmans of other people's positions.

Being good at communicating philosophical ideas is a separate skill and one I can't advise you on.

I think the most basic philosophical skill is understanding past arguments. Reading Plato and Aristotle is good practice for this, because their books have a lot of subtle arguments that don't require much previous tradition. Then maybe you'll start reading later stuff, making your own arguments and tracing them through the literature, talking to people and so on.

Or if you don't find the fun in reading all these arguments - then maybe just leave it. The same thing could happen in any other area, like math or physics or programming. Feynman famously said about physics that "it may give some practical results, but that's not why we do it". Annie Dillard makes a similar point:

A well-known writer got collared by a university student who asked, "Do you think I could be a writer?"

"Well," the writer said, "I don’t know…. Do you like sentences?"

The writer could see the student’s amazement. Sentences? Do I like sentences? I am twenty years old and do I like sentences? If he had liked sentences, of course, he could begin, like a joyful painter I knew. I asked him how he came to be a painter. He said, "I liked the smell of the paint."

For me personally, some arguments from classical philosophy are fun (learning as recollection and so on), but not so much fun that I'd like to do it as a career.

I think there are very distinct skills in "philosophy", which have different measures for achievement/skill, and therefore different training regimens.  Like most things one might want to get better at, there are specializations to consider.  Analogously, you can train in "sports" to a certain level, but beyond that you train in "track and field", and beyond that "javelin throw".

So, what do you actually want to get better at, and where are you starting from?

Parts of logical presentation of arguments can be trained as debate, and others as blog posts or published articles.  

Philosophical history and comparative studies of populations are probably best practiced in academia.

Actual useful models of human behaviors and justifications that many give for those behaviors - probably best practiced in the doing.   

I think there are two parts to being good at philosophy: argumentative skill and cached knowldge.

Cached knowledge is knowing a given topic, the arguments around it and so on. Without cached knowledge you can't engage in a real discussion because you have to reinvent the wheel while other people are discussion the best design for a car. Getting cached knowledge is largely a matter of reading existing work and discussion with people who know the field

Argumentation is being able to argue well. This means spotting flaws in arguments, being able to distinguish between an argument being true and being important, finding the cruxe(s) of a discussion and so on. This is hard to learn and is more a skill. The best way to learn it in my experience is lots and lots of practice with short feedback cycles and direct, clear feedback. Competitive debating can help. So can the standard route of writing lots of papers and having someone who is good mark them and rip them apart when/where they're unpersuasive/unclear/imprecise.