Using both classical and quantum mechanical Monte Carlo methods, a number of properties are investigated for a single hydrogen atom adsorbed on palladium and nickel clusters. In particular, the geometries, the preferred binding sites, site specific hydrogen normal mode frequencies, and finite temperature effects in clusters from two to ten metal atoms are examined. Our studies indicate that hydrogen is localized in the present systems. The preferred hydrogen binding sites are found to be tetrahedral in clusters with five or fewer metal atoms and octahedral for clusters of six to ten atoms. The exceptions to this rule are Ni9H and Pd9H for which the outside, threefold hollow and the inside tetrahedral sites are preferred, respectively. Hydrogen induced "reconstruction" of bare cluster geometries is seen in seven and ten-atom clusters.