State-of-the-art nanolithography machines employ extreme ultraviolet (EUV) light to pattern nanometer-scale features on silicon wafers for the production of integrated circuits. This radiation is generated in a laser-produced plasma formed on tin microdroplet targets. This thesis presents work on radiation-hydrodynamic simulations of tin droplet-based laser-produced plasmas, including plasma characterization, plasma expansion, and subsequent early-time droplet dynamics. The work is closely connected to experimental measurements, be it to successfully validate the simulation results on plasma expansion and droplet dynamics, or to guide future experiments towards optimal EUV emission conditions. It is shown that, after validation, the simulations can provide additional insight into (i) non-trivial plasma dynamics leading to the measured ion kinetic energy distributions and (ii) the plasma impulse shaping the early-time droplet dynamics that ultimately determines the late-time droplet morphology. Moreover, the simulations can successfully explore a broad range of laser wavelengths and intensities. Finally, these investigations aim to complement efforts to increase the performance of the EUV source system: the conversion efficiency of laser pulses to in-band EUV radiation as well as the lifetime of the collector mirror, which may be affected by ionic or liquid debris.