The algorithm of the calculations of all principal kinetic characteristics of nucleation of supercritical droplets under the gradual creation of the metastable state in vapor (total number of emerging droplets, beginning time and duration of droplet emergence, and dimensions of droplets) was formulated. It was shown that under the given properties of the vapor - gas medium, the liquid condensing from it, as well as at given dimensions of condensation nuclei, the algorithm allows us to cover the entire range of the characteristic time of the creation of the metastable state in vapor and that of the initial concentration of the condensation nuclei admitted by the conditions of the theory applicability. It was elucidated that the macroscopicity of condensation nuclei results in more rigorous conditions of applicability. Based on the algorithm, numerical calculations demonstrated the ability of the theory proposed to make practical prospects in a rather wide range of external parameters of the theory. The theory was generalized for the case of the gradual creation, arbitrarily changing in time, of the metastable state in vapor.