The value of the equilibrium constant for a particular reaction under specific conditions may be determined by experiment. The only data required would be the concentrations of all products and reactants once the system has reached equilibrium.
In practice it is generally not necessary to measure all of the substances. If the initial amounts of substances are known and the final amount of just one can be determined, it is then possible to determine the concentrations of all other species by following the stoichiometry of the reaction. More about that later.
The simplest possible calculation of the value of Kc would be by plugging given values into the correct expression.
Simple calculations can give some idea of what the equilibrium constant is all about but they only go so far. It would be helpful to know a bit more about how the constant can be used to make predictions about a system or to compare two systems.