Based on thermodynamic investigations a general scenario of first-order phase transitions in finite systems starting from metastable initial states is developed. It is shown that at least three different main stages of this process can be distinguished: a stage of nucleation and simultaneous growth of the already formed supercritical clusters; a stage of relatively independent growth of the dusters, their number being nearly constant; and a stage of competitive growth, of Ostwald ripening, leading to a decrease in the number of clusters and an increase in their mean radius. A kinetic description of the different stages and the whole course of the phase transition is given. The influence of the depletion of the medium on the nucleation rate is taken into account in terms of a quasi-steady-state nucleation rate. The growth of the clusters is described by a general growth equation derived in preceding papers. It is shown that the mean radiusrα in the stage of independent growth varies with time as (for diffusion-limited growth) orrα ∼ t (for kinetic-limited growth). Differential equations for the mean radius, the number of dusters, and the total volume of the new phase as functions of time are obtained for the whole course of Ostwald ripening including the initial stage. In the asymptotic region the solutions of these equations are in agreement with the results of Lifshitz, Slyozov, Wagner, and others. The results of our analysis confirm the necessity, as first suggested by Binder and Stauffer, of taking into account in nucleation theories the possible simultaneous growth of the already formed supercritical clusters. Based on thermodynamic investigations a new definition and a new interpretation of the completion time first introduced by these authors are given.