Molecular dynamics simulations are used to investigate the dissolution of NaCl nanocrystals (containing similar to 2400 ions) in water. We focus on systems under sink conditions at 300 K, but the influences of concentration and temperature are also investigated. Cubical, spherical, tablet-shaped, and rod-shaped nanocrystals are considered, and it is shown that the initial shape can influence the dissolution process. Dissolution is observed to occur in three stages: an initial period where the most exposed ions are removed from the crystal surface, and the crystal takes on a solution-annealed shape which persists throughout the second stage of dissolution; a second long intermediate stage where dissolution roughly follows a fixed rate law; and a final stage where the small residual crystal (less than or similar to 200 ions) dissolves at an ever increasing rate until it disappears. The second stage of dissolution which applies for most of the dissolution process is well described by classical rate equations which simply assume that the dissolution rate is proportional to an active surface area from which ions are most easily detached from the crystal. The active area depends on the initial crystal shape. We show that for our model NaCl nanocrystals the rate-determining step for dissolution under sink conditions is ion detachment from the crystal, and that diffusion layers do not exist for these systems.