This article presents the tradition of phenomenologically founded psychological research that was originally initiated by Amedeo Giorgi. This data analysis method is inseparable from the broader project of establishing an autonomous phenomenologically based human scientific psychology. After recounting the history of the method from the 1960's to the present, we explain the rationale for why we view data collection as a process that should be adaptable to the unique mode of appearance of each particular phenomenon being researched. The substance of the article is then devoted to a detailed outline of the method's whole-part-whole procedure of data analysis. We then offer a sample analysis of a brief description of an ordinary daydream. This is an anxiety daydream in response to the recent Covid-19 pandemic. We present this daydream analysis in full to show the concrete hands-on 5 step process through which the researcher explicated the participants' expressions from the particular to the general. From this brief sample analysis, the researcher offers a first-person reflection on the data analysis process to offer the reader an introduction to the diacritical nature of phenomenological psychological elucidation.