The left brain is easier to describe since it's all about words. The left brain has a narrower, more focused, and 2D view of the world. It only sees a small inner portion of the right visual field, corresponding to the small area of the cones.
The right brain is always finding things for the left brain to attend to. It mostly does this by turning the head and eyes to look at something. Whatever is inside the visual plane at the time of looking is either recognized or decomposed by the left brain into smaller bits until some bit is recognized. Left brain recognition consists of mapping the recognized bit(s) into a set of symbols. This is often done with context provided by the right brain.
The left brain carries a huge number of symbols, and it keeps track of a large number of relationships among the symbols. So the right brain is able to recognize a plant, but it might not be able to recognize what to do with a seldom- or never-seen plant without the left brain turning some of the details of the plant, like leaf shape or color, into symbol references and connecting them to symbolic references to other plants in memory. The left brain combines the recognized and referenced symbols to form a sense of the new plant and create a new symbol to represent the plant.
The left brain doesn't create a new symbol for everything new it encounters. If a new item is deemed to be very much like another, it will adapt the previous symbol to stand for both things. This involves making connections from the new bits it encountered to the adapted symbol and modifying the adapted symbol to include the new bits. Thus, every time we encounter a new tree, our symbolic understanding of 'tree' enlarges to include it. So while the right brain is busy remembering the true image of the new tree, the left brain is remembering the new bits of the new tree and generalizing 'tree' to be even less like any real tree than it was before.
Most of the left-brain symbols are associated with verbal terms. I say "terms" because the association may be with either a word or a phrase (or a collection of words or phrases.) When a symbol is activated by sensory input, the word(s) and phrase(s) are conjured along with the symbol.
The left brain operates at two levels. The previous paragraphs describe the first level, in which the limited sense inputs of the left brain activate symbols and create new ones. The second level 'plays' with this rich symbol collection, informed by the activation of symbols by the first level. This playing goes on all the time, sometimes directed by symbol activation ("I see the cat") and sometimes operating without sensory input (daydreaming.) And many parts of the left brain may be playing simultaneously with different sets of symbols.
The second level of left brain activity is what we normally think of as consciousness. It is a jumble of individual words, fleeting thoughts, story lines, planning, reviewing, judging, etc., all happening at once. The elements of the jumble typically involve words, lots of words, competing for attention.
The primary attribute of all these verbal mental processes in the left brain is that they are all based on the left brain symbols, not sensory input directly. McGilchrist in Master and Emissary calls this use of the symbols "re-presentation" in order to differentiate it from direct perception ("presentation" of the world). This is one of the attributes that makes the left brain so powerful: it can see and play with a world that doesn't exist. But it also separates the left brain from reality. The symbols are always approximations of reality, sometimes differing substantially from it, and this can lead to problems.
One of the ways the left brain connects its symbols is linearly, as if in time. I say "as if" because the left brain's concept of time is strictly "ordering", not flow. Time in the left brain is discrete and not continuous. Events unfolding over time in the world become in the left brain a discrete series of symbolic events. This (re)ordering of events is especially useful for planning and carrying out plans. The left brain can "play" with the ordering of events, even constructing orderings that it hasn't encountered before. Then it can step through such a series of events and carry out very precise processes that have never been seen before.
With all the verbal mayhem going on in the left brain, there has to be a way for attention to be focused. In a previous post I referred to this process as "choosing" without going into what it involves. In practical terms "choosing" involves activation levels of neural networks in the left brain. Each neural network corresponds to one of the elements in the verbal jumble referred to earlier. The activation level of a neural network depends on many factors: the strength and number of symbol activations, the emotional impact of the activations, and the state (mood) of the brain (meaning what other networks are activated.) Not least is habituation, in which activations that we experience more tend to happen more. Unless a network is continually reinforced, its activation decays with time, so it will likely be replaced by another network/thought/idea/concept. Thus our attention moves from thing to thing.
One of our many choices is to attend to the right brain view directly. When this happens, the words stop, we notice our peripheral vision, and other senses may report. We almost always then notice something interesting. The right brain will usually direct the eyes to it, which almost always activate a left-brain, verbal network enough to start some story ("That's a cumulus cloud".) So we tend not to attend directly to the right brain's view for very long before we find ourselves attending to one of the many neural patterns in the left brain.
One characteristic of left-brain activity is that it takes a bit of time. Sensory input has to activate symbols, which in turn activate multiple neural nets, which then have to be arbitrated among, each step of which takes time. While the right brain can mediate appropriate responses to stimuli in a handful of milliseconds ("duck!"), the left brain can take hundreds of milliseconds to appropriately attend. Thus, our normal lives (walking, driving, lovemaking, etc.) are mediated by the right brain. At the same time the right brain is performing these actions, the left brain is participating as a voyeur. This leaves it free to think about things that have nothing to do with the activity at hand or create stories about the activity that may not be entirely true. Even if it attends and doesn't prevaricate, its experience is at best a series of symbol activations.
This brings us to a central conundrum: the left brain lies. When you ask a person about an activity, it is the left brain that responds, because it controls speech. To answer the question the left brain will have to mediate among various activations that occurred during the activity, and the right brain view is only one of them. The choice of what activation to report is a complex consideration of survival, advantage, habit, time to respond, and myriad other factors. If the measure is objective reality, only the right brain view is true, and the left brain may not choose to report it.