Solid lattices of weakly coupled magnetic molecules provide an unique opportunity to study magnetism at a nanoscale level. Each non interacting molecule in the lattice represents a single nanomagnet composed of only a few magnetic moments. These magnetic moments are coupled to each other via exchange interaction. The overall magnetic properties of molecules are entirely ascribed to these few magnetic moments. In order to investigate the spin dynamics of these systems as a function of temperature and external magnetic field we performed an extensive experimental investigation using nuclear magnetic resonance (NMR) and muon rotation spectroscopy (muSR) techniques. The aim of this study is to characterize and understand the collective behavior of a system of interacting magnetic moments as the temperature and external field are changed. This characterization can be done by using various types of nuclei as local microscopic magnetic probes. In fact the nuclear magnetic moments are coupled via hyperfine interactions to the electronic magnetic moments, therefore by measuring nuclear magnetic parameters such as the NMR line width, the nuclear spin-spin and spin-lattice relaxation rates T-12 and T-11 or the muSR muon depolarization rate we can indirectly obtain various types of microscopic magnetic information. In this thesis we present experimental data pertaining to a wide variety of different molecular magnets, characterized by several different parameters such as the number and value of the localized magnetic moments, the spatial arrangement of these moments inside each molecule and the intensity of the intra molecular exchange coupling. In particular we have addressed the influence of these parameters on the nuclear relaxation and depolarization rates and investigated several different effects.