We present Spitzer imaging of the metal-deficient (Z ~30% Z_sun) Local Group dwarf galaxy NGC 6822. On spatial scales of ~130 pc, we study the nature of IR, H alpha, HI, and radio continuum emission. Nebular emission strength correlates with IR surface brightness; however, roughly half of the IR emission is associated with diffuse regions not luminous at H alpha (as found in previous studies). The global ratio of dust to HI gas in the ISM, while uncertain at the factor of ~2 level, is ~25 times lower than the global values derived for spiral galaxies using similar modeling techniques; localized ratios of dust to HI gas are about a factor of five higher than the global value in NGC 6822. There are strong variations (factors of ~10) in the relative ratios of H alpha and IR flux throughout the central disk; the low dust content of NGC 6822 is likely responsible for the different H alpha/IR ratios compared to those found in more metal-rich environments. The H alpha and IR emission is associated with high-column density (> ~1E21 cm^-2) neutral gas. Increases in IR surface brightness appear to be affected by both increased radiation field strength and increased local gas density. Individual regions and the galaxy as a whole fall within the observed scatter of recent high-resolution studies of the radio-far IR correlation in nearby spiral galaxies; this is likely the result of depleted radio and far-IR emission strengths in the ISM of this dwarf galaxy. ; Comment: ApJ, in press; please retrieve full-resolution version from http://www.astro.wesleyan.edu/~cannon/pubs.html