Here's a brain dump on the topic. This is the fruit of about 50 years noodling around on the subject from all angles with all sorts of "systems", teachers and traditions, so take it FWIW.
Meditation is often presented in a vastly over-complicated way, sometimes overblown, sometimes under-estimated. It's quite simple in principle (though it's got tremendous depth, and does require commitment, in practice). There are two aspects to it, or two sides to the coin of it (I'm using the formulation of Mahayana Buddhism, but it's really the same in all systems, because it's grounded in commonalities re. how the brain/mind works):-
1. "Calming" meditation - quite simply, this is just getting the body into parasympathetic activation mode, while the mind remains alert and awake. The nervous system has two modes of activation, sympathetic and parasympathetic, sympathetic is the normal waking state, in which the mind and body are geared to interacting with the world around you. Parasympathetic activation is the body "shutting down" in order to self-repair - most obviously in sleep, but sometimes just dozing off can get it too. The key is that in meditation you have activate the parasympathetic nervous system but also at the same time keep the mind awake and alert - and that's tricky, because normally when the body "drops" into parasympathetic activation (it's a notable sensation that you can sometimes catch in the act while falling asleep), the mind shuts down too (i.e. one falls asleep). The required alertness is obtained by sitting upright and keeping the spine absolutely straight, but while the body is relaxed, and that is effected by getting the right tilt to the pelvis, which is effected by using a cushion and sitting cross legged (in one of several possible ways) with the knees lower than the hips. There are lots of other options, but this is what one might call the "classic" method that's common across many traditions.
In the calm state, you are alert and awake, aware of what's going on around you, but not reacting to it, and the mind is naturally fairly empty of thoughts, while the body is deeply relaxed, with the breath naturally slow, refined, minimal and even. Also, the body is somewhat "blank" in terms of sensations - one might say it's the proprioceptive equivalent of "brain grey" for the visual system when the eyes stop saccading, or have the same input wherever they saccade (e.g. if you either fixate on an object, or stare at a blank wall). The more practiced you are at calming meditation, the more naturally empty of thoughts the mind will get, and quicker too (i.e. at first it might take 5-10 minutes to get the "drop", eventually it's instant, and profoundly deep, as soon as you sit down to your accustomed posture).
There are many, many ways to
mechanically get the body into a parasympathetic state (e.g. body scanning, focusing on the breath, counting breaths, fixating on an object, staring at a blank wall, etc.) and there are all sorts of refinements, but that's the basic idea.
2. "Insight" meditation. This is what you "do" while you're in the calm state, and there are roughly two types of things to do in the calm state: 1) rational investigation, and 2) passive observation of subjective experience.
Rational investigation is, for example, analyzing the philosophical teachings of a traditional school like Buddhism or Daoism, or even something like the method of Cartesian doubt, but in the sense of how they apply to you and your personal experience, rather than as mere arguments (as we would do with philosophy here). Essentially one "tests" the teachings in one's own experience, with one's mind as a laboratory of sorts. Particular attention may be paid to the question "Who/what am I?" and this is one of the most powerful methods, as it attacks the central problem directly. But meditations on transience, death, etc., are also valuable.
Passive observation is to simply be aware of the world without thinking of what it is, what it's called, without conceptualizing it. You suspend your knowledge of what this "thing", your experience, is, but you nevertheless attend to it carefully in the here and now. One charming simile used in the Tibetan teachings is of a child wandering a temple. The kid doesn't know what the hell these golden statues of gods, etc.,
are, but it's hypnotized by their beauty. That's the thing you want, that suspension of naming and conceptualization, that
not-knowing, while still being minutely focused on the texture of experience in the here and now.
By either route, or alternating both, and with sufficient depth of calm, at some point - usually, though not invariably, after a period of intense fear, or of feeling like you're close to losing your mind - it occurs to you that you don't exist in the way you've been accustomed all your life to thinking you exist. It occurs to you that you are not an independent entity imprisoned in the body, sitting somewhere behind the eyes peeping out at the world. The ordinary everyday sense of "I", "me", etc., vanishes, or one might say it becomes diaphanous, or insignificant. At the same time, there's a concomitant realization that "your" consciousness isn't personal, but rather
impersonal, i.e. it "belongs" to the Universe, it's not just the body's consciousness, but also the property of the Universe at large.
Initially, this experience can be either bland or an absolutely stunning revelation, it's different for different people and at different times. How it's described in different cultures and in different times varies as well - some cultures have been plain and analytical about it, some have been more florid and "religious" in describing it. The emotional feeling-tone of the insight in its full form is one of immense, profound peace, "the peace that passeth understanding." (Note: this is different from the sense of calm that arises with parasympathetic activation, it's a mental phenomenon, the result of having come up to the buffers, so to speak, to a
full stop, with no more questions, with all possible questions of the "big" variety answered.)
It's the same realization whether the context is religious or a-religious, theistic or non-theistic, or rationalist. (The religionist simply views the experience as revelatory of a direct link to the Divine - the bit of God, who is omnipresent, that's in you, so to speak; the rationalist can take a more abstract view that it's simply a kind of intimacy with the Universe at large, or even more simply, an absence of the sense of separation.)
Notably, insight can be had without the benefit of calming meditation, in ordinary everyday circumstances, or in peak/flow experiences (such as skilled sports, or drug experiences) or in moments of stress, grief, fear, etc. - but it's usually fleeting, evanescent, and often passed over as of no significance, or rejected as something fearful (some forms of what's been called "depersonalization" are probably insight experiences). Calming meditation stabilizes the insight so that it's more fully grasped. Also, insight deepens calm, and calm facilitates insight - they go together rather nicely and help each other along.
Having this experience is only the beginning - obviously the ultimate aim is to live in the world from this perspective. And that's where the "teachings" of all the great religions come from. Were we simply rational animals, ethics would remain at the level of virtue ethics. The larger dimension of ethics, the sense of universal brotherhood, etc., comes from this area,
comes from people who have experienced this type of experience. (Of course these are not contradictory - universalist ethics must be built on a solid foundation of virtue ethics, otherwise it becomes an insane kind of hyper-altruism. In fact the practice of virtue ethics is a necessary preliminary practice for meditation in most traditional systems, since if the mind is constantly disturbed by reflection on wrongdoing, it's difficult for it to get into a calm state.)
One thing to watch out for, a major pitfall, is this:
the disappearance of the ordinary sense of self is not itself the goal, and it's a common trap to think it is, to make an enemy of the ordinary everyday sense of self, and to strive to be in a "state" of no-self all the time. That's a false goal, pseudo-enlightenment. In fact, it's perfectly fine to have that ordinary, everyday sense of self. The trick is to know at all times, with unshakeable certainty, that it's not real,
even while it seems to be. That is full, final enlightenment, at least according to some Buddhist and Advaita traditions. Having the experienc eof the disappearance of the ordinary sense of self is a big help, a big initiation, and with that experience one finally has one's foot in the door, so to speak; but the disappearance
per se of the ordinary sense of self is not the goal. Again, traditional teaching similes come to our aid: in the dark, one mistakes a coiled rope for a snake. Upon investigation, one realizes it's a coiled rope, and one then remains unshakably certain that it's not a snake, but a coiled rope,
even if it still looks like a snake.
This is basically what it's all about. As I say, it can be elaborated in various ways and there are lots of possible ramifications that can be explored, and it's something you can get better at in various ways, but this twofold procedure is the core "thing" of meditation, and the "royal road" that's common to many traditions in the East
(Note: the West had similar teachings in antiquity - for example, there's a practice called "incubation" which was used as a form of healing and psychotherapy in the ancient Greek world, which involved lying down in a dark place and simply
giving up - under supervision and with the guidance of trained attendants. Parmenides' teacher was said to have taught him "silence." The West's teachings had to go underground as a part of "occultism" during the time of Catholicism's doctrinal and political hegemony, and often got garbled as a result. It should be noted that, like some Chinese Daoist systems, and Tibetan systems like Dzogchen, the Western systems tended to favour "astral travel", which is basically lucid dreaming entered into from the waking state. This "astral travel" is what "magick" is all about - it's what generated the various "apocalypses" and "visions" you find in things like the Gnostic teachings, as well as things like the "visionary" proem to Parmenides' philosophy, which reads, quite literally like a straightforward account of a vision, and is itself an introduction to the philosophy, rather than just some flowery, irrelevant preamble.)