This happens through osmosis. By allowing a higher concentration of some solute out of the cell (likely through active or facilitated transport.) the concentration of the solute is higher outside of the cell than inside. Water exits the cell through diffusion of water (osmosis) to create equilibrium where there is an equal amount of solute both inside of the cell and outside.
This figure shows the addition of salt to fresh water on one side of the membrane causes water to move to the other side. Salt cannot go through the membrane unassisted but water can. Many organisms use channel proteins which can be opened or closed to allow certain molecules into or out of the cell. This is referred to as facilitated diffusion or active transport when energy is required.