The superposed pair of spiral galaxies making up NGC 3314 offers a unique opportunity to trace the dust properties in a spiral galaxy. We analyze multicolor Hubble Space Telescope imaging, supported by ground-based near-IR imaging and fiber-array spectroscopy, to measure dust extinction in the foreground Sc galaxy NGC 3314A, which is backlit by the Sb system NGC 3314B. The superposition allows us to measure extinctions over a wide range of galactocentric radii in the foreground galaxy from 0.4-4.5 kpc. In the outer half of the disk, the extinction is strongly localized in discrete dust lanes, including some patches whose galactic setting is clear only because of associated Hα emission at the foreground velocity. These dust features show an extinction curve with a slope close to the Galactic mean (R=3.5+/-0.3) over a range in galactocentric radius from 1.6 to 3.8 kpc, with no radial trend. Using the I-K color of the background nucleus, we derive an extinction of AI=3.3 through the disk at a projected distance of 400 pc from the nucleus of NGC 3314A. The extinction in even the inner disk of NGC 3314A is quite patchy, since background Hα emission is detected from all parts of the system. Local anticorrelations between foreground and background line emission demonstrate that the dust is concentrated in star-forming regions, as has been found for the blue light in several systems. The colors of the dust lanes in NGC 3314A that are projected only partially against the background disk indicate that the dust scale height in the foreground disk is substantially smaller than that of the stars. The color-intensity behavior of the net light in these regions tracks the predictions of a thin-layer model closely. Based on observations with the NASA/ESA Hubble Space Telescope obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.