The principles of process-oriented guided inquiry learning (POGIL) are applied to the analysis of the emission spectrum of atomic hydrogen. Over the course of three learning cycles, students construct the hydrogen atom's energy level diagram and assign quantum numbers using their measurements of the Balmer series plus additional information on the emission lines in the Lyman and Paschen series. This guided inquiry approach to the hydrogen emission spectrum, which was developed as part of the POGIL Physical Chemistry Laboratory Project, has been tested at several institutions with a variety of spectroscopic instruments. The analysis leading to the assignment of quantum numbers requires simple and inexpensive supplies: rulers, colored pens, and long strips of paper.