In-depth investigations of the low energy electronic structures of mononuclear lanthanide complexes, including single molecule magnets, are challenging at the best of times. For magnetically coupled polynuclear systems, the task seems well nigh impossible. However, without detailed understanding of the electronic structure, there is no hope of understanding their static and dynamic magnetic properties in detail. We have been interested in assessing which techniques are most appropriate for studying lanthanide single-molecule magnets. Here we present a wide ranging theoretical and experimental study of the archetypal polynuclear lanthanide single-molecule magnet Dy3 and derive the simplest model to describe the results from each experimental method, including high-frequency electron paramagnetic resonance and far-infrared spectroscopies and cantilever torque magnetometry. We conclude that a combination of these methods together with ab initio calculations is required to arrive at a full understanding of the properties of this complex, and potentially of other magnetically coupled lanthanide complexes.