Barfield calls the early peoples' common sense "original participation," in that with their sense perceptions there was an extra-sensory participation with the object being sensed. While it is difficult to know what original participation is "like," there are some indications of it in our experience. Barfield mentions feeling panic—a fear that goes beyond what the actual situation warrants. Another might be sexual attraction. Another might be the feeling of emotion from hearing instrumental music. As for what thinking was like at that time, I suspect we could relate that to the thinking of children before they acquire egos at about age six. As mentioned, something like original participation can be understood when we converse. We "hear through" the words to the meaning behind the words, and hence our minds participate with each other. In our current state, which Barfield calls "final participation," that participation with the objects we sense still exists (otherwise there would be no perception at all), but has moved from the outside into our subconscious. All we experience consciously is the surface form of the object, like words of an unknown language, meaningless to us. The mentality within, or behind the object is blocked out. We thus treat the surface form as the whole object, like worshipping a statue of God in place of what the statue represents—hence the subtitle of Barfield's book: A Study in Idolatry.
And:
Why is it, he asks, that all of our vocabulary for mind has been taken from the vocabulary for nature? Why did the Greeks have just one word, 'pneuma,' which we must variously translate as 'spirit' or as 'wind' (or 'breath')? And of course the Latin root of 'spirit,' inspiritus, also meant breath. The same goes for most all of our vocabulary for mental activity. The explanation is simple: the ancients simply did not differentiate between our two meanings. That is, in ancient common sense, wind is spirit.
via Idealism vs. Common Sense, a guest essay on Bernardo Kastrup's site.
[Edit... Hmmm, now this is getting more interesting. A later review of this article reveals that I missed some of the real depth here. There is a link in this article with another fascinating insight revealed in the work of Ken Biegeleisen, whose book talks about how the great transformation, in multiple cultures around the world, which began around 600 BC, can be traced to the Diaspora from Israel at that time, as people carried monotheism and certain economic and cultural practices from Jerusalem into other cultures: 
This thought is developed a little further, and apparently moreso in the original Barfield essay, and then the writer goes into a philosophical speculation that closely aligns with some of my own thought experiments, eventually leading to his conclusion, where he proposes the next step in the evolution of consciousness, when we all become conscious in a whole new way:
And what of uncontrolled nature? Recall that "final participation," as Barfield calls it, doesn't mean the end of participation, rather that participation has moved from appearing outside of ourselves, as it did in original participation, to being a subconscious process inside of us. Hence we can consider the possibility of that process becoming conscious. We will then be conscious of the creative process that produces nature's outward forms. Which is to say that what is now a collective subconscious would become a collective consciousness. We would be experiencing how we—human minds and the minds behind natural phenomena—are collectively creating the reality we perceive.
Now couple this with Korzybski's insight on how there is a large change for the better when we learn to remove the logical flaw of identity from our thinking. Lastly, take a look at what D.G. Leahy does with "the thought currently being expressed." Is Leahy's approach opening the door to a way the collective subconscious can communicating openly, basically thereby becoming the collective consciousness described here? I think so.
Well worth pursuing further.