Individuation is discussed in philosophy and psychology, and everyone defines it a little differently. It's perhaps most famous for its use in Jungian Psychology, and that's what we're interested in here. Jung defined individuation as the process by which an individual differentiates themself from their Personality Type. Jung describes it as an unconscious process, one that happens spontaneously over which we have little control, but also refers to work that can be done to integrate unconscious material into consciousness to encourage individuation.
So what does that mean? Essentially, it means an individual's personality will grow out of the caricature of its definition by experience, and transform into a unique self. Specifically, we will grow by experience that encourages us to deal with the shadow aspects of our personality so that these dark and mysterious parts of ourselves become conscious and we begin to understand them.
For example, an Extraverted Thinker (ESTJ, ENTJ) does not understand Introverted Feeling, and often rejects it (and people whose personalities are dominated by it) as selfish and ridiculous. Introverted Feeling is the shadow function of the Extraverted Thinker, and exists only in the unconscious where it has a dark and scary aspect. If the Extraverted Thinker is strongly related to an Introverted Feeler, through marriage or family connection or whatever, the ET will recognize some value in the Introverted Feeler, and eventually might experience an epiphany, after which they will consciously understand what Introverted Feeling is all about, and that it has value.
The transformation caused by the "epiphany" is individuation. It may occur as a result of dreams, or engaging in active imagination, or holding the tension of the opposites until understanding occurs, which is perhaps the most common way most of us will experience individuation. In the example above, the Extraverted Thinker learned to hold the idea that Introverted Feeling might have value, while maintaining his personality's perspective that Introverted Feeling has no value. Stewing with these opposite beliefs caused a new, individuated understanding to occur.
Jung contended that moments of individuation happen for most of us throughout our lives, and that is how we grow and rise above the weaknesses of our personality types, and become wholly functioning individuals.
“The ego keeps its integrity only if it does not identify with one of the opposites, and if it understands how to hold the balance between them. This is possible only if it remains conscious of both at once. However, the necessary insight is made exceedingly difficult not by one’s social and political leaders alone but also by one’s religious mentors. They all want decisions in favor of one thing, and therefore the utter identification of the individual with the necessarily one-sided truth.”
Holding the tension of the opposites is an important concept for anyone interested in individuation. However comforting it is to us to believe strongly in the truth and righteousness of one side over another, holding contradictory beliefs and views in our consciousness at the same time gets us closer to global truth. Doing so will facilitate the process of individuation, and our consciousness, wholeness and wisdom will grow.
Dream diariesJung refers to dreams as "a spontaneous self-portrayal in symbolic form of the actual situation in the unconscious." Our dreams are messages from our subconscious, and if we pay attention to them, we can learn many things.
The best way to bring our dreams into our conscious minds is to keep a dream diary next to our beds, and write down dreams as soon as we wake up. This requires dedication, but is a proven method for constellating unconscious material into consciousness, thus encouraging the process of individuation.
Active imaginationIn the Jungian sense, active imagination is an act of meditation during which an individual focuses on an image or feeling. Usually, these images and feelings are inspired by dreams, but they don't have to be. One might imagine speaking with a character they dreamed of, or meditating on a strong feeling a dream brought about.
More detail on active imagination
HypnosisJung used hypnosis fairly extensively with his mentally-ill patients, which he called "hypnotic suggestive therapy," mostly as a means of suggesting behavioral changes to the subconscious mind. Eventually, he eschewed using hypnosis as a means of encouraging individuation, although he continued to use it to mitigate problematic behavior. If Jung were alive today and familiar with modern types of hypnotherapy, he would probably be a proponent.
Jung did some controversial things in his quest for constellating unconscious material. He was into Tarot, not because he believed in fortune telling, but because he found the images on the cards to be very similar to the archetypal images of the subconscious, and believed that interacting with those images could spur unconscious activity.
He was greatly impressed with the "dignity and serenity" of a Native American Hopi tribe who he spent some time with in Taos, New Mexico. He believed they were strongly connected to the Collective Unconscious, primarily due to their coherent system of beliefs and their ritualistic practices that supported those beliefs, which included the use of peyote. The beliefs themselves were secondary to their way of life, in which they professed to "think with their hearts rather than their heads." Jung himself was a rational man, and no doubt the discoveries he made with the Hopi led him to constellate some of his own unconscious material.
Jung believed that the use of psychedelic drugs provides access to unconscious material, but there is evidence that he was against their use in the general population. In a letter to Father Victor White, Jung wrote that many users of psychedelics were not ready to face to contents of the unconscious, and that they might be "haunted" by its ghosts and left to struggle with the darker aspects of their psyche. It's not clear whether or not Jung was under the influence of psychedelic drugs when he created The Red Book, but it certainly seems probable.