Molecular simulations of crystal nucleation and growth from an evaporating salt solution are presented. Despite the fact that crystallization from solution is the most common way of producing crystals in nature, it has not been simulated on a computer with molecular resolution. We show that such calculations are feasible both for clusters and for extended systems, containing initially an almost saturated solution of sodium chloride. Moreover, we demonstrate that, within a broad range of external conditions, the nanosecond time scale computer simulations robustly and reproducibly display the onset of salt crystallization from solution. We also provide analysis at an atomic resolution and establish the role of water molecules in the process. The present simulations provide unique information about the mechanism and dynamics of nucleation and crystal growth from an evaporating solution. Such information can be used for predictions of morphologies and growth rates of macroscopic crystals from first principles.