Growing interest in exploring mechanically mediated biological phenomena has resulted in cell culture substrates and 3D matrices with variable stiffnesses becoming standard tools in biology labs. However, correlating stiffness with biological outcomes and comparing results between research groups is hampered by variability in the methods used to determine Young's (elastic) modulus, E, and by the inaccessibility of relevant mechanical engineering protocols to most biology labs. Here, we describe a protocol for measuring E of soft 2D surfaces and 3D hydrogels using atomic force microscopy (AFM) force spectroscopy. We provide instructions for preparing hydrogels with and without encapsulated live cells, and provide a method for mounting samples within the AFM. We also provide details on how to calibrate the instrument, and give step-by-step instructions for collecting force-displacement curves in both manual and automatic modes (stiffness mapping). We then provide details on how to apply either the Hertz or the Oliver-Pharr model to calculate E, and give additional instructions to aid the user in plotting data distributions and carrying out statistical analyses. We also provide instructions for inferring differential matrix remodeling activity in hydrogels containing encapsulated single cells or organoids. Our protocol is suitable for probing a range of synthetic and naturally derived polymeric hydrogels such as polyethylene glycol, polyacrylamide, hyaluronic acid, collagen, or Matrigel. Although sample preparation timings will vary, a user with introductory training to AFM will be able to use this protocol to characterize the mechanical properties of two to six soft surfaces or 3D hydrogels in a single day.