An atomic force microscope (AFM) fundamentally measures the interaction between a nanoscale AFM probe tip and the sample surface. If the force applied by the probe tip and its contact area with the sample can be quantified, it is possible to determine the nanoscale mechanical properties (e.g., elastic or Young's modulus) of the surface being probed. A detailed procedure for performing quantitative AFM cantilever-based nanoindentation experiments is provided here, with representative examples of how the technique can be applied to determine the elastic moduli of a wide variety of sample types, ranging from kPa to GPa. These include live mesenchymal stem cells (MSCs) and nuclei in physiological buffer, resin-embedded dehydrated loblolly pine cross-sections, and Bakken shales of varying composition. Additionally, AFM cantilever-based nanoindentation is used to probe the rupture strength (i.e., breakthrough force) of phospholipid bilayers. Important practical considerations such as method choice and development, probe selection and calibration, region of interest identification, sample heterogeneity, feature size and aspect ratio, tip wear, surface roughness, and data analysis and measurement statistics are discussed to aid proper implementation of the technique. Finally, co-localization of AFM-derived nanomechanical maps with electron microscopy techniques that provide additional information regarding elemental composition is demonstrated.