Conjugated polymers show promising properties as cheap, sustainable and solution-processable semiconductors. A key challenge in the development of these materials is to determine the polymer chain structure, conformation and packing in both the bulk polymer and in thin films typically used in devices. However, many characterisation techniques are unable to provide atomic-level structural information owing to the presence of disorder. Here, we use molecular modelling, magic-angle spinning (MAS) and dynamic nuclear polarisation surface-enhanced NMR spectroscopy (DNP SENS) to characterise the polymer backbone group conformations and packing arrangement in the high-mobility donor-acceptor copolymer diketopyrrolo-pyrrole-dithienylthieno[3,2-b]thiophene (DPP-DTT). Using conventional 1H and 13C solid-state MAS NMR coupled with density functional theory calculations and molecular dynamics simulations, we find that the bulk polymer adopts a highly planar backbone conformation with a laterally-shifted donor-on-acceptor stacking arrangement. DNP SENS enables acquisition of 13C NMR data for polymer films, where sensitivity is limiting owing to small sample volumes. The DNP signal enhancement enables a two-dimensional 1H-13C HETCOR spectrum to be recorded for a drop-cast polymer film, and a 13C CPMAS NMR spectrum to be recorded for a spin-coated thin-film with a thickness of only 400 nm. The results show that the same planar backbone structure and intermolecular stacking arrangement is preserved in the films following solution processing and annealing, thereby rationalizing the favourable device properties of DPP-DTT, and providing a protocol for the study of other thin film materials.