Shamanism is not a religion. It is a healing technology.
Shamanic healing is humanity's oldest healing system, going back perhaps as much as 40 thousand years. That it has persisted so long, and in essentially the same form across many cultures, is a testament to its effectiveness. While indigenous shamanism is always embedded in its culture, the many elements that are common across the world's cultures can be studied and practiced in the context of our own culture. Michael Harner was one of the first to do this; he set up the Foundation for Shamanic Studies to train and teach practitioners, and to aid indigenous peoples wishing to regain a lost shamanic heritage.
Shamanic healing is based on the idea that there are spirits. That is, non-physical entities that seem to be conscious, and that it's possible for some people to interact with them. In Shamanism, the specially skilled person (called the shaman) travels in trance to the worlds where the spirits live, with the mission of getting help or information, for healing his or her clients and the whole community. In particular, there are compassionate spirits that have an interest in helping humans reduce the load of suffering in this world. The shaman learns where in the spirit worlds to find these compassionate spirits, and develops a partnership with them for this work.
While it's easy to dismiss the idea of spirits as "unscientific", the work is practical and effective. All the world's cultures have a rich folklore around the idea of spirits -- with many parables of both the trouble you can get yourself into, and the good that you can do, by exploring the spirit worlds. Whether there are "really" spirits or not is perhaps unimportant -- the idea is a powerful and effective metaphor. Shamanic healing work is a highly disciplined approach to the spirit worlds. The shaman is focused on a mission during the trance -- learning to hold this focus in the trance state is the essence of shamanic training. Once the shaman returns from trance, he or she is completely back.
In almost all of the world's cultures that have a shamanic tradition, the shaman will go into trance with the aid of monotonous drumming, or other similar percussion. In this trance, he or she will travel to the spirits in their realm -- hence the term journey. A few traditions use psychoactive plant extracts, but drumming has been found to be equally effective, and it's much easier to end the trance when needed!
Interestingly, the layout of the spirit worlds, as seem by shamans in all the world's cultures, is remarkably similar. (I take this as evidence that there is "actually" a spiritual reality, independent of culture, that they are independently visiting.)
Shamanic healing is almost always done in close partnership with the shaman's helping spirits. The shaman relies on these spirits for information, guidance, power, and protection. The spirits rely on the shaman as a physical intermediary and compassionate helper. There are roughly four main kinds of shamanic healing:
Sandra Ingerman (see her web site for books and seminars) developed this technique on her own, then discovered that it was essentially identical to what indigenous shamans had been doing for eons. She is now widely regarded as the formost authority on soul retrieval. She has refined the technique over the years, in thousands of sessions, to the gentle and effective practice it is today.
I have experience with several different masters in this field -- Michael Harner of the Foundation for Shamanic Studies , Brazilian Spiritists Carlos and Maria Lucia Sauer (incidentally, I do not know their current contact information), and Betsy Bergstrom.
In traditional cultures, shamans perform other (related) work as well: