The design of a downlink communication system for returning scientific data from an interstellar flyby probe is reviewed in this tutorial white paper. It its assumed that the probe is ballistic, and data is downloaded during a period following encounter with the target star and its exoplanet(s). Performance indices of interest to scientific investigators include the total launch-to-completion data latency and the total volume of data reliably recovered. Issues considered include the interaction between the speed and mass of the probe and the duration of downlink transmission. Optical communication using pulse-position modulation (PPM) with error-correction coding (ECC) is assumed. A very large receiver collection area on or near Earth is composed of individual incoherently-combined diffraction-limited apertures. Other important issues in the design including transmit and receive pointing accuracy and beam size and receiver field of view are reviewed. Numerical examples assume a mission to Proxima Centauri (the nearest star to our Sun) initially launched by directed-energy propulsion from the vicinity of Earth.