An apparatus and method for cleaning fabrics, floor coverings, and bare floor surfaces utilizing a soil transfer cleaning medium is disclosed. A method of mechanically removing soil from a surface intended to be cleaned includes the steps of successively and repeatedly: wetting a portion of a cleaning medium with a cleaning liquid; extracting any soil and at least some of the cleaning liquid from the previously wetted portion of the cleaning medium; and wiping the surface intended to be cleaned with the portion of the cleaning medium so as to transfer soil from the surface intended to be cleaned to the cleaning medium. Portable and vehicle-based devices may be utilized to practice the method of cleaning.