An approximate semianalytic theory is developed to describe the homogeneous nucleation of droplets from a supersaturated vapor, beginning with a partition function and including rigorously the translation and surface tension contributions. The liquid and vapor phases are treated as uniform (step density profile) and may be described by any accurate equation of state. It is shown that the classical approximation for the free energy of droplet formation may be derived from the present theory by making additional approximations (ideal gas, incompressible liquid), and the two are compared for the case where the vapor phase forms a reservoir (constant supersaturation). In the case of a finite-sized vapor phase, where the supersaturation decreases as the droplet grows, a free energy minimum exists beyond the critical radius, and this stable droplet equilibrium is examined in detail. Comparison with computer simulations proves the quantitative accuracy of the present theory for a Lennard-Jones system. Also derived is a new, formally exact expression for the surface tension that is useful for computer simulations.