Well The fact that you're asking this question only shows your prejudiced attitude towards everything that is being put forward. All the talks about the nature of higher cognition had no other purpose than to elucidate this "how". Since you're still asking "how" I take it that you have formed a quite limited conception of what higher cognition actually is and what it reveals. Seems that what is called higher cognition is for you only speculative mosaic of thoughts about the unknowable higher world - that is, theology.
I'll try one final attempt with an analogy, that I take from Ashvin's essay here - that of dreaming and waking consciousness. I must stress that it's only an analogy, there are many different things when we speak about actual higher vs. waking consciousness (waking vs. dreaming in our analogy).
The first thing is to overcome the prejudice that there's a hard boundary between dreaming and waking consciousness (read - waking and higher consciousness). We know that our dreams can be influenced by happenings in the external world. For example, if it's really hot in my bedroom this may be experienced in the dream as if I'm trying to escape out of a burning building. Let's imagine that we become somewhat lucid in the dream and realize that our dream persona, our environment, etc. are only images for deeper processes of reality. This would correspond to the popular notion of enlightenment. Yet in itself, it doesn't present any details about these deeper processes but just the clear idea that our environment is only the shadow of reality. We need to go further than this if we are to investigate the depths of reality and how exactly they project into the shadow dream picture. It is clear that if we simply recombine in the most ingenious ways our dream content this will not lead us to waking consciousness but only to more complicated dream-models of it. Now if we are in the dream and someone speaks about rhythms, patterns, beings of higher life which are responsible for the dynamics of the dream pictures, we can say "that's an interesting model but no one can know these things. It's nothing but speculative thinking, a rationalization of the higher reality."
This is pretty much the situation today. It's generally accepted that the sensory realm truly is only the surface projection of a deeper reality but anything claiming that there's a possibility to penetrate in this depth is regarded with the greatest doubt.
The waking vs. dream analogy is not very good and that's why I very rarely resort to it. Because of the superficial thinking of our age, this analogy usually causes more confusion than explanation. One of the things is that both in our dream and waking life we operate with a similar intellectual mode of cognition. If the analogy is taken too literally this makes it look like the higher world simply changes the contents of our perceptions yet we remain more or less the same intellectual ego. This already makes it difficult to point attention to the higher forms of cognition because for this we need to reveal the higher forces which animate the intellect on a lower level.
You say every time that I repeat the same things for the 101th and 201th time but that's only because the point is missed over and over again. I hope that the above analogy can help at least for this - to place things in their proper relations. It's not about demeaning or preaching anything. It's simply the only way one can speak of these things if we need to be true to the facts. Yes, the dream consciousness is a permanent aspect within which the impermanent dream images come and go. But we place a bet if we think that the causes of the impermanent images are none of our dream-world's business (or if we think that the causes are wholly contained within the dream, as in materialism). So there are two things:
1. The nature of spiritual science is completely misunderstood because it's viewed only as conceptual speculation about the reality responsible for the dream imagery. The fact that through self-development is possible to increase lucidity and awaken in the higher world and trace the sources of the dream images - including our dreaming self - is outright dismissed as impossible and subject to the fundamental limits of knowledge. That's the reason for your "how" question. We've been speaking of nothing else than this "how" all the time but it's simply not taken seriously. It's preferred to see everything as elegant theory (Platonic or otherwise) but it's too insulting to consider that such knowledge can proceed from actual experiences from the waking world.
2. Even if the nature of spiritual science is understood (for which I don't see indications since you're still asking the "how" question) one can still say "well, maybe there's a reason why we feel disconnected from the higher world. This is what we chose to experience. We are messing where we are not supposed to if we try to bridge the dreaming and waking life." One can no doubt take such a position. Yet it's the duty of those who have some direct knowledge of the waking world to say something about the repercussions of ignoring the bridge. This bridge connects us not to some remote world but to what we really are in our subconscious depths. In the dream we have a body, name, temperament, desires, opinions, inclinations, yet we take these for granted. Penetration into the waking world reveals first and foremost the forces that shape our dream character. With this immediately become clear the reasons for the pitiful state of humanity today. Humans are ignorant of their spiritual nature, have all kinds of excuses that this nature is a taboo not to be messed up with, and that's how misery perpetuates.
I'm skeptical that all the above will make any difference but I do it to be clean with my conscience, that I've done everything in my power to present these things as clearly as possible.