Ab initio calculations at the MP2 and coupled cluster levels have been performed for small clusters of hydrogen molecules. A concise model interaction potential was constructed on the basis of ab initio potential surface points for the dimer and on comparison with ab initio results for the trimer and tetramer. The model was used to investigate key features of cluster growth, starting with the aggregation energies for clusters with up to 10 molecules. Fully anharmonic zero-point vibrational energies were evaluated for these clusters and were found to be a sizable fraction of the well depth for small clusters. Calculations on larger clusters were used to follow the approach to regular structures in large aggregations, the energetics of cluster growth, and the internal rotation potential for hydrogen molecules embedded in a large cluster. It was found that the essentially free rotation involves concerted reorientation of hydrogen molecules in the first surrounding shell.