The study of thermoelectric materials spans condensed matter physics, materials science and engineering, and solid-state chemistry. The diversity of the participants and the inherent complexity of the topic mean that it is difficult, if not impossible, for a researcher to be fluent in all aspects of the field. This review, which grew out of a one-week summer school for graduate students, aims to provide an introduction and practical guidance for selected conceptual, synthetic, and characterization approaches and to craft a common umbrella of language, theory, and experimental practice for those engaged in the field of thermoelectric materials. This review does not attempt to cover all major aspects of thermoelectric materials research or review state-of-the-art thermoelectric materials. Rather, the topics discussed herein reflect the expertise and experience of the authors. We begin by discussing a universal approach to modeling electronic transport using Landauer theory. The core sections of the review are focused on bulk inorganic materials and include a discussion of effective strategies for powder and single crystal synthesis, the use of national synchrotron sources to characterize crystalline materials, error analysis, and modeling of transport data using an effective mass model, and characterization of phonon behavior using inelastic neutron scattering and ultrasonic speed of sound measurements. The final core section discusses the challenges faced when synthesizing carbon-based samples and the measuring or interpretation of their transport properties. We conclude this review with a brief discussion of some of the grand challenges and opportunities that remain to be addressed in the study of thermoelectrics.