The definitive practice of Zen is meditation and koan analysis. Both aim at dissociating a practitioner from his ingrained pattern of rational thinking. Zen however does not aim at cultivating irrational thought. The theory is that our ingrained patterns of rational thinking will distort our perception. We cannot see our “true self”. To be enlightened we need to break away from such constraints so that we can see our “true self”. Such constraints broadly speaking come from two areas: firstly it is constrained by the concepts we use to understand the world around us, these concepts we learned in our socialization process and solidified by our interactions with our environment which includes people and things; secondly it is constrained by our Unconscious (as understood in Freudian psychoanalysis, a subject worth studying by interested readers).
To be freed from our conceptual constraints, a Zen practitioner questions the assumptions used in our rational thoughts which are presented in the form of the language we use. The process is very much like the process of philosophizing as used in academic analytic (or linguistic) philosophy. We can never get to the bottom of truth of anything but each step of our questioning moves us closer to a state where there are lesser and lesser pre-suppositions and assumptions. Failing to practice "koan analysis/philosophizing" renders an “enlightened master” incapable to move back to “normal everyday life” without being re-constrained by his concepts, his conditioned way of thinking and language . Fair to say nowadays Zen practitioners do less philosophizing than in those in Dynasty China. Some modern Zen texts have a wrong conception: “koan is for seated meditation”. In actual practice it is “thinking clearly” or “philosophizing with a clear mind” on koan, rather than doing seated meditation while analyzing a particular koan, which is an impossible task to do without failing in either (meditation or analysis).
The practice of Zen meditation is not the same as Mindfulness training, as used popularly. I prefer calling the former “deep meditation” to differentiate it from Mindfulness which is getting more popular (because as "advertised": it is easy-to-do)! The possibility of doing deep meditation presupposes the practice of chi-meditation (as trained in tai chi and chi kung) that opens our joints and connects our internal sensation into a holistic chi-sensation that encompasses our entire body. That will take quite a number of years to perfect for the average practitioner (The classic texts said it would be easier for people under the age of sixteen when our body is still growing). After this foundation chi-training, a meditator can get into a dream-like zone while he is doing seated meditation and he will also have some vivid dreams during his normal sleep.
Such dreams (including normal dreams and dreams in meditative dream-like zone) will be vivid for the simple reason that one’s body is chi-connected during seated meditation and (to a lesser extend) during normal sleep.
The special thing about vivid dream in Zen practice is that one can feel the “reality” of such experience. With a chi-filled body, his Unconscious comes to meet his rational mind. Conflicts can therefore be resolved instead of being repressed. With a good understanding of Buddhism, Taoism or psychoanalysis a practitioner can navigate his “healing process” or “enlightenment process” while he sees his inner psychic development as revealed in his successive dreams (that progresses to resolve conflicts or dissolve away rational constraints or whatever, as defined differently in different practice). Such process is called individuation in Jungian psychology and enlightenment in Zen.
The practice of dream analysis is, needless to say, another topic.
(revised on 29 Dec 17)