The most important procedures about the scientific investigation of Unidentified Aerial Phenomena (UAP) using astronomy-like methods are conceptually presented and discussed, where results obtained in the past are triggering the proposal for new observational sessions using multiwavelength and multimode instruments. A special emphasis is posed on the techniques of magnetometry, photometry and spectroscopy, and on the importance of studying the variability of the phenomenon in order to try to understand the physical process that governs it, including a possible propulsion mechanism. The most important obtainable physical parameters are discussed in detail, with a particular emphasis on how they might be correlated together. The idea of placing measurement instruments at areas of the world where the phenomenon is recurrent is strongly suggested. Past monitoring campaigns at such locations are punctually mentioned together with the pertinent literature. In addition to the natural, manmade and the extraterrestrial hypotheses used to explain the nature of UAPs, the “plasma life” hypothesis is ventured too.