The paper presents the results of molecular dynamics (MD) simulation of the kinetics of spontaneous crystallization of a supercooled Lennard-Jones (LJ) liquid. In the study of nucleation, the mean lifetime method, direct forward flux sampling, and the seeding approach were used. The nucleation rate, the number of particles in a critical nucleus, the diffusion coefficient of nuclei in the space of their sizes, and some other parameters have been determined. Calculations have been made along four isobars in the region of positive and negative pressures and three isotherms of temperatures higher and lower than that of the triple point. In the nucleation rate, the interval from 10(-200) to 10(-6) was overlapped (in units of (epsilon/m)(1/2)/sigma(4), where sigma and epsilon are parameters of the LJ potential and m is the particle mass). The results of calculations have been compared with classical nucleation theory (CNT) without accounting for the size dependence of the effective surface free energy of a crystal nucleus. The dependence of the effective surface free energy of a critical nucleus gamma(e) on its size has been determined by the results of MD simulation from CNT. Calculations have been made of the first two coefficients of expansion of gamma(e) into a series in terms of the curvature of the dividing surface-an analogue of the Tolman length and a parameter that determines the size dependence of the Tolman length in isothermal and isobaric processes.