A Monte Carlo model is developed for the hopping conductance in arrays of quantum dots (QDs). Hopping is simulated using a continuous time random walk algorithm, incorporating all possible transitions, and using a nonresonant electron-hopping rate based on broadening of the energy levels through quantum fluctuations. Arrays of identical QDs give rise to electronic conductance that depends strongly upon level filling. In the case of low charging energy, metal insulator transitions are observed at electron occupation levels, , that correspond to the complete filling of an S, P, or D shell. When the charging energy becomes comparable to the level broadening, additional minima in conductance appear at integer values of , as a result of electron-electron repulsion. Disorder in QD diameters leads to disorder in the energy levels, resulting in washing out of the structure in the dependence of conductance on and a net reduction in conductance. Simulation results are shown to be consistent with experimental measurements of conductance in arrays of zinc oxide and cadmium selenide QDs that have different degrees of size disorder, and the degree of size disorder is quantified. Simulations of the temperature dependence of conductance show that both Coulombic charging and size disorder can lead to activated behavior and that size disorder leads to conductance that is sublinear on an Arrhenius plot.