We examine and visualize cluster formation, nucleation, and growth by Monte Carlo simulations in the three-dimensional Ising model at T/T-c=1/4, i.e., far from the critical temperature. Homogeneous nucleation rates as a function of supersaturation are obtained. From the slope of nucleation rate curves, model-free values for the critical cluster size are calculated, which agree with predictions of the Gibbs-Thomson relation for cubic nuclei. In fact, examining the shape of the critical clusters more closely, we find them to be cubical rather than spherical. Accordingly, the work of nucleus formation is accurately given by the classical nucleation theory, at least for the 3D-Ising model at the relatively low temperatures examined here. Furthermore, from the simulations subcritical equilibrium cluster number distributions are determined, which also agree with predictions for the exponential part of the classical nucleation theory.