We describe a system for rapidly measuring the brightness of the night sky using a mosaic of CCD images obtained with a low-cost automated system. The portable system produces millions of independent photometric measurements covering the entire sky, enabling the detailed characterization of natural sky conditions and light domes produced by cities. The measurements are calibrated using images of standard stars contained within the raw data, producing results closely tracking the Johnson V astronomical standard. The National Park Service has collected hundreds of data sets at numerous parks since 2001 and is using these data for the protection and monitoring of the night-sky visual resource. This system also allows comprehensive characterization of sky conditions at astronomical observatories. We explore photometric issues raised by the broadband measurement of the complex and variable night-sky spectrum, and potential indices of night-sky quality.