Dense micron-sized electron plasmas, such as those generated upon irradiation of nanostructured metallic surfaces by intense femtosecond laser pulses, constitute a rich playground to study light-matter interactions, many-body phenomena, and out-of-equilibrium charge dynamics. Besides their fundamental interest, laser-induced plasmas hold great potential for the generation of localized terahertz radiation pulses. However, the underlying mechanisms ruling the formation and evolution of such plasmas are not yet well understood. Here, we develop a comprehensive microscopic theory to predictably describe the spatiotemporal dynamics of laser-pulse-induced plasmas. Through detailed analysis of electron emission, metal screening, and plasma cloud interactions, we investigate the spatial, temporal, and spectral characteristics of the so-generated terahertz fields, which can be extensively controlled through the metal morphology and the illumination conditions. We further describe the interaction with femtosecond electron beams to explain recent ultrafast electron microscopy experiments, whereby the position and temporal dependence of the observed electron acceleration permits assessing the associated terahertz field. Besides its potential application to the design of low-frequency light sources, our work contributes fundamental insight into the generation and dynamics of micron-scale electron plasmas and their interaction with ultrafast electron pulses.