Context. This is the first of a series of investigations into far-IR characteristics of 11 planetary nebulae (PNe) under the Herschel Space Observatory open time? 1 program, Herschel Planetary Nebula Survey (HerPlaNS). Aims. Using the HerPlaNS data set, we look into the PN energetics and variations of the physical conditions within the target nebulae. In the present work, we provide an overview of the survey, data acquisition and processing, and resulting data products. Methods. We performed (1) PACS/SPIRE broadband imaging to determine the spatial distribution of the cold dust component in the target PNe and (2) PACS/SPIRE spectral-energy-distribution and line spectroscopy to determine the spatial distribution of the gas component in the target PNe. Results. For the case of NGC? 6781, the broadband maps confirm the nearly pole-on barrel structure of the amorphous carbon-rich dust shell and the surrounding halo having temperatures of 26-40? K. The PACS/SPIRE multiposition spectra show spatial variations of far-IR lines that reflect the physical stratification of the nebula. We demonstrate that spatially resolved far-IR line diagnostics yield the (Te, ne) profiles, from which distributions of ionized, atomic, and molecular gases can be determined. Direct comparison of the dust and gas column mass maps constrained by the HerPlaNS data allows to construct an empirical gas-to-dust mass ratio map, which shows a range of ratios with the median of 195 ± 110. The present analysis yields estimates of the total mass of the shell to be 0.86? M?, consisting of 0.54? M? of ionized gas, 0.12? M? of atomic gas, 0.2? M? of molecular gas, and 4 × 10-3? M? of dust grains. These estimates also suggest that the central star of about 1.5? M? initial mass is terminating its PN evolution onto the white dwarf cooling track. Conclusions. The HerPlaNS data provide various diagnostics for both the dust and gas components in a spatially resolved manner. In the forthcoming papers of the HerPlaNS series we will explore the HerPlaNS data set fully for the entire sample of 11 PNe.