We mapped NGC 6946 in continuum dust emission at 100, 160, and 200-mu-m with a He-3 cooled array of 32 bolometer detectors, and in the g band, r band, and H-alpha + [N II] with a large-format CCD camera. The beam-widths of the far-infrared camera were 45" at 100 and 160-mu-m and 56" at 200-mu-m; the optical images were smoothed to the resolution of the far-infrared images. Also, we present maps of the galaxy at 12, 25, and 60-mu-m, made with 1' resolution from Infrared Astronomical Satellite (IRAS) data processed with a Lucy-Richardson deconvolution algorithm. Continuum dust emission is studied in relation to spiral and radial structure, to the distribution of the interstellar medium, and to ionizing and nonionizing radiation from stars. This paper attempts to clarify the sources of dust heating, the optical and spectral characteristics of the nuclear source and disk, the properties of dust grains, and the origins of infrared luminosity in NGC 6946. The 60, 100, 160, and 200-mu-m continuum distributions show discrete sources coinciding with giant H II regions superposed on a smooth, unresolved disk background which decreases exponentially with radius. Sources which coincide with giant H II region complexes are more prominent relative to the disk at shorter wavelengths; a few sources brightest at 160 and 200-mu-m indicate dust grains cooler than 18 K. Emission parameters T, beta, and tau-(100), derived from the far-infrared continuum data, vary with position in the disk. Sixty-four percent (7.5 x 10(9) L.) of the stellar luminosity in the central 45", and 35% (3.4 x 10(10) L.) in the central 5', is absorbed by dust; also, we estimate that 25% (5.3 x 10(10) L.) of the total stellar luminosity in the disk is absorbed by dust. Approximately 5% of the total 160-mu-m luminosity originates beyond the 25 mag arcsec-2 blue isophote, where dust temperatures are less than 18 K. Infrared luminosities of cool dust (approximately 15-24 K) in quiescent interstellar gas, and warm dust (> 29 K) in complexes of massive star formation, are estimated with a two-component model. The distribution of infrared emission from cool dust (25%-30% of the total infrared luminosity of the galaxy) agrees with the results of an analytic model describing transport of stellar photons in the neutral interstellar medium. Stars having m < 10 M. embedded in optical depths for visual absorption of 0.5 or less cover an estimated 90% of the total surface area of the galactic disk; these stars generate 70% of the total stellar luminosity, or approximately 60% of the total bolometric luminosity.