Observations over the past year have yielded detailed information on the eclipsing millisecond pulsar PSR 1957+20 and its orbiting companion. We have found the pulsar to be similar in many ways to other millisecond pulsars: its spin parameters are extremely stable, its period derivative is very small (1.61 + 0.09 × 10-20), its profile has a strong interpulse, and its radio spectrum has a steep power-law index of about -3. The orbit is nearly circular, with an eccentricity less than 2 × 10-5, and the mass function implies a companion mass not much greater than 0.022 M⊙. Eclipses last for approximately 56 and 50 minutes at 318 and 430 MHz, respectively, corresponding to a ν-0.41±0.09 dependence of eclipse duration on frequency, at least over this small range. Excess delays of the pulsed signal near the edges of eclipse depend on frequency approximately as ν-2 and vary substantially from one eclipse to another. The average pulse profile shows weak circular and almost no linear polarization. An absence of measurable Faraday delays between left and right circularly polarized components implies that the mean longitudinal magnetic field is no more than a few gauss in the region just outside the eclipsing material. The available evidence points strongly toward a system in which radiation from the pulsar heats the companion to the point of ablation, thereby driving a stellar wind that trails outward and behind the companion, somewhat like a comet tail. The lack of measurable change in the orbital period of the system suggests a time scale for evaporation of the companion greater than 107 yr.