Free energies of ion hydration have been evaluated by using the thermodynamic integration technique (the slow growth method) in molecular dynamics simulations. Ionization processes of Na, Ca, and Cl have been considered. The cutoff method and the Ewald summation approach have been used alternatively in truncating the long-range electrostatic interactions. The extended simple point charge (SPC/E) model [J. Phys. Chem. 91, 6269 (1987)] and the ion-water potential of Straatsma and Berendsen [J. Chem. Phys. 89, 5876 (1988)] have been used in out simulations. The results have been tested against experimental measurements and the Ewald method has led to the best performances. A good agreement with the Born model was found in the charging process of a calcium ion. Changes in the organization of water molecules around the ion have been evaluated from equilibrium molecular dynamics simulations performed at different stages of this process. Ion-water radial distributions functions, and the orientation of water molecules as well as residence times have been analyzed.