The Hertzsprung-Russell diagram (HRD) is a fundamental representation in stellar physics. It contains information about key properties of stars and allows inferences about stellar evolution. The use of the HRD is an important disciplinary activity in astrophysics. For example, it is particularly important to have a graphical understanding of the HRD in order to understand elementary astrophysical relationships (e.g., about the luminosity, temperature, radius, and mass of stars). However, several research papers indicate that students often have difficulty interpreting the HRD, apparently due to its visual complexity, and a number of learning difficulties have been described. Yet, there is still no evidence concerning how learners actually select and extract information from the HRD when completing tasks. In this study, we examined the gaze patterns and think-aloud protocols of 35 physics students as they performed 14 open-response tasks. Benchmarking against traditional x-y diagrams shows that the HRD imposes a significantly higher cognitive load on students, particularly due to the representation of luminosity, magnitude, and spectral class. Students reported a variety of learning difficulties related to information selection and extraction, sometimes mechanistically copying procedures from typical x-y diagrams. Eye-movement analysis confirmed these learning difficulties on a procedural level and show whether the students fixated on task-relevant parts of the HRD. Based on the study results, preliminary recommendations can be made in order to create engaging learning materials relating to the HRD.