Equilibrium constants are determined in order to quantify chemical equilibria. When an equilibrium constant  is expressed as a concentration quotient,  
it is implied that the activity quotient is constant. For this assumption to be valid, equilibrium constants must be determined in a medium of relatively high ionic strength. Where this is not possible, consideration should be given to possible activity variation.
The equilibrium expression above is a function of the concentrations [A], [B] etc. of the chemical species in equilibrium. The equilibrium constant value can be determined if any one of these concentrations can be  measured. The general procedure is that the concentration in question is measured for a series of solutions with known analytical concentrations of the reactants. Typically, a titration is performed with one or more reactants in the titration vessel and one or more reactants in the burette. Knowing the analytical concentrations of reactants initially in the reaction vessel and in the burette, all analytical concentrations can be derived as a function of the volume (or mass) of titrant added.
The equilibrium constants may be derived by best-fitting of the experimental data with a chemical model of the equilibrium system.