A Journey of Acquisition is performed by both the Priest Kings and the Kurii. The Priest-Kings accomplish this for the task of purely obtaining new genetic material for the Goreans while the Kurii perform it as a way of establishing further spies into the Priest-Kings world for obtaining strategic information, population figures, current state of technology, warfare, and subterfuge or espionage.
The primary method of a journey is through the use of a specific fleet of the Priest-Kings designed for space travel to and from Earth. These starships, designed to house Earth humans for processing, medical cleansing, and catalouging, go to Earth about every few years, usually a minimum of 5 or more years between each Journey, and capture individual females.
Most often, a capture has been described by Earth females as being intercepted in an enclosed or wide open area with little to no human population or interaction. They are captured most often alone and vulnerable such as when sleeping or otherwise focused on something that robs them of all perception. A sense of confusion, hallucinations, and dizziness precedes the actual capture. It is theorized that Priest-Kings use some form of hallucinogenic paralytic to capture females. After this, a feeling of weightlessness and then a bright white light before unconsciousness is perceived.
The females are then taken aboard the vessels in orbit around Earth, hidden from the massive collection of sensors and satellites by Earth's governments and organizations, then proceed to Gor. Once around Gor's orbit, they transport the females at random locations on the planet, but always within a few miles of Gorean populations so that they may be easily discovered and captured.
Kurii use a similar method of retrieval, but their purpose is much more specific. They desire to create hidden spies within the general populace. Most often, they are transported to specific population centers or regions of Gor where they require more pertinent information. It is not currently known if the Kurii do anything specific to the Earth females or if they use a similar method of transport like the Priest-Kings.
It should be clarified that most of this is based on theory and supposition as not all information concerning the Journeys are fully understood by the official content from the novels.