To design and engineer materials inspired by the properties of the brain, whether for mechanical simulants or for tissue regeneration studies, the brain tissue itself must be well characterized at various length and time scales. Like many biological tissues, brain tissue exhibits a complex, hierarchical structure. However, in contrast to most other tissues, brain is of very low mechanical stiffness, with Young's elastic moduli E on the order of 100s of Pa. This low stiffness can present challenges to experimental characterization of key mechanical properties. Here, we demonstrate several mechanical characterization techniques that have been adapted to measure the elastic and viscoelastic properties of hydrated, compliant biological materials such as brain tissue, at different length scales and loading rates. At the microscale, we conduct creep-compliance and force relaxation experiments using atomic force microscope-enabled indentation. At the mesoscale, we perform impact indentation experiments using a pendulum-based instrumented indenter. At the macroscale, we conduct parallel plate rheometry to quantify the frequency dependent shear elastic moduli. We also discuss the challenges and limitations associated with each method. Together these techniques enable an in-depth mechanical characterization of brain tissue that can be used to better understand the structure of brain and to engineer bio-inspired materials.