The stability constant of metal complexes is actually an equilibrium constant that describes the overall process of the formation of a metal complex in a solution.
This formation process is usually a substitution reaction in which one ligand replaces another ligand. In your case, EDTA, which is a hexadentate ligand (it has 6 lone pairs of electrons), replaces water, a simple ligand.
The overall reaction looks like this - all the species are in aquesous solution, except water, of course
To write the stability constant for this reaction you can use the same rules as you would for writing classic equilibrium constants - the concentrations of the products (water is excluded) divided by the concentration of the reactants