The Arcetri Near Earth Object Precovery Program (ANEOPP) is a project dedicated to the identification of images of Near Earth Objects (NEOs) on past archival materials, an activity usually referred to as precovery. Going years back in time to locate such images results in the acquisition of very good orbital information, which, in turn, allows astronomers to perform more accurate studies of the dynamical evolution and physical characterization of NEOs, as well as improve assessments of their impact hazard. We discuss the tasks involved in this work and the basic techniques used to yield successful identifications on photographic plates. Begun in mid-1999, ANEOPP has precovered more than 70 NEOs to date, which were previously observed only during the discovery apparition. The keys to obtaining these results have been: i) easy access to competitive collections both in digital form and as plastic copies; ii) traveling to additional collections; iii) the recent development of reliable algorithms to determine the boundaries of the recovery region, which is the portion of the celestial sphere where an asteroid with an uncertain orbit can be found at a given time.