In this paper we present a theoretical study of the ground and excited surface states of an excess electron on isolated dielectric and metal clusters. An electron-cluster model potential, which consists of a short-range repulsive interaction with a strength V-0 much greater than 13.6(a(0)/R)(2) eV (where R is the cluster radius) and a long-range polarization potential, was used to explore the cluster size dependence and the dielectric constant (epsilon) dependence of the energetics and charge distribution of the electron surface states. Scaling relations were used for the quantification of the cluster size dependence of the physical properties near the localization threshold and for the bridging between the energetics on a cluster microsurface and a flat macrosurface. The onset of the cluster size for localization in the ground 1s (n = 1, l = 0)-electronic state is characterized by a "critical" cluster radius R(c)((10)) similar or equal to 2.02(1-Q)a(0)/Q, where Q = (epsilon - 1)/4(epsilon + 1). Information on electronic spectroscopy was inferred from the cluster size and epsilon dependence of the transition energies. The behavior of an excess electron on metal clusters and on composite clusters (metal core coated by a He or Ne microsurface) will provide information on the size dependence of the dielectric constant and on the metal-nonmetal transition in large finite systems.