Meditation (especially Zen meditation) in the western world, aims for the attainment of a quiet mind. Meditation training teaches one to cease thinking and ‘float’ in the state of ‘bliss’ or in the emptiness of a ‘gap’ whilst still being aware of the environment. Meditation usually takes place within beta brainwave patterns (30-13 Hz)

Contemplation is the method of focusing thought with an open mind toward the understanding of something, and, as such, requires both inspirational and analytical mind processes in the alpha and beta brainwave frequencies.

Prayer is a form of talking, usually requesting, aimed at a higher, divine power. Often a prayer is recited, sung or chanted and is the active part of conversation, with contemplation as a form of the listening half. Prayer takes place mainly in the left hemisphere at beta frequencies. Repeated chanting can put one in a trance or alpha state.

Hypnosis / self-hypnosis primarily takes place in alpha brainwave states (8-13 Hz), somewhat deeper and slower than beta yet slightly higher than pre-sleep theta waves (4-8 Hz). It utilizes primarily the right brain hemisphere with it’s imaginative and inspirational abilities to visualize and know either new ideas or old ones in new ways. Hypnosis by-passes our conscious tendency to filter information and allows reprogramming of ingrained thought patterns.

Trance or Theta states are similar states to deep hypnosis, taking place in the alpha/theta brain wave frequencies.

Check out what Wikipedia says about altered states of consciousness.