As different proteins have different compositions of amino acids, different protein molecules precipitate at different concentrations of salt solution.
Unwanted proteins can be removed from a protein solution mixture by salting out as long as the solubility of the protein in various concentrations of salt solution is known.
After removing the precipitate by filtration or centrifugation, the desired protein can be precipitated by altering the salt concentration to the level at which the desired protein becomes insoluble.
One demerit of salting out in purification of proteins is that, in addition to precipitating a specific protein of interest, contaminants are also precipitated as well. Thus to obtain a purer protein of interest, additional purification methods such as  ion exchange chromatography may be required.