Understanding and actively controlling the spatiotemporal dynamics of nonequilibrium electron clouds is fundamental for the design of light and electron sources, high power electronic devices, and plasma-based applications. However, electron clouds evolve in a complex collective fashion on the nanometer and femtosecond scales, producing electromagnetic screening that renders them inaccessible to existing optical probes. Here, we solve the long-standing challenge of characterizing the evolution of electron clouds generated upon irradiation of metallic structures using an ultrafast transmission electron microscope to record the charged plasma dynamics. Our approach to charge dynamics electron microscopy (CDEM) is based on the simultaneous detection of electron-beam acceleration and broadening with nanometer/femtosecond resolution. By combining experimental results with comprehensive microscopic theory, we provide a deep understanding of this highly out-of-equilibrium regime, including previously inaccessible intricate microscopic mechanisms of electron emission, screening by the metal, and collective cloud dynamics. Beyond the present specific demonstration, the here-introduced CDEM technique grants us access to a wide range of nonequilibrium electrodynamic phenomena involving the ultrafast evolution of bound and free charges on the nanoscale.