Layered delta-MnO2 (birnessites) are ubiquitous in nature and have also been reported to work as promising water oxidation catalysts or rechargeable alkali-ion battery cathodes when fabricated under appropriate conditions. Although tremendous effort has been spent on resolving the structure of natural/synthetic layered delta-MnO2 in the last few decades, no conclusive result has been reached. In this Article, we report an environmentally friendly route to synthesizing homogeneous Cu-rich layered delta-MnO2 nanoflowers in large scale. The local and average structure of synthetic Cu-rich layered delta-MnO2 has been successfully resolved from combined Mn/Cu K-edge extended X-ray fine structure spectroscopy and X-ray and neutron total scattering analysis. It is found that appreciable amounts (similar to 8%) of Mn vacancies are present in the MnO2 layer and Cu2+ occupies the interlayer sites above/below the vacant Mn sites. Effective hydrogen bonding among the interlayer water molecules and adjacent layer O ions has also been observed for the first time. These hydrogen bonds are found to play the key role in maintaining the intermediate and long-range stacking coherence of MnO2 layers. Quantitative analysis of the turbostratic stacking disorder in this compound was achieved using a supercell approach coupled with anisotropic particle-size-effect modeling. The present method is expected to be generally applicable to the structural study of other technologically important nanomaterials.