Anthropologist here. Shamanism relies on altering one's mental state to widen their perception and come into touch with whatever higher powers they believe in. It's not a specific form of religion, but rather a means to an end. Many different religions across the world use shamanistic methods to pursue their spiritual goals.
A shaman is one who takes these spiritual journeys and sometimes brings others along in opposition to many faiths wherein a mass trusts a leader's word as truth.
While many spiritual paths rely on the teachings of a master, shamanism is very individualistic and ultimately left up to the perceptions of the shaman. Unfortunately, many modern practitioners use shamanism as an excuse for drug consumption without fully understanding the religious nature of the practice.
Some popular examples of shamanism include the consumption of ayahuasca or peyote. In fact, the classic white and red fly agaric/amanita "magic mushroom" is/was used by Sami shaman in Northern Fennoscandia. Some argue that the tradition of Christmas reindeer is loosely derived from this practice.