The giant elliptical galaxy NGC 1316 (Fornax A) is a well-studied member of the Fornax Cluster and a prolific producer of Type Ia supernovae, having hosted four observed events since 1980. Here we present detailed optical and near-infrared light curves of the spectroscopically normal SN 2006dd. These data are used, along with previously published photometry of the normal SN 1980N and SN 1981D, and the fast-declining, low-luminosity SN 2006mr, to compute independent estimates of the host reddening for each supernova, and the distance to NGC 1316. From the three normal supernovae, we find a distance of 17.8 +/- 0.3 (random) +/- 0.3 (systematic) Mpc for Ho = 72. Distance moduli derived from the "EBV" and Tripp methods give values that are mutually consistent to 4 -- 8%. Moreover, the weighted means of the distance moduli for these three SNe for three methods agree to within 3%. This consistency is encouraging and supports the premise that Type Ia supernovae are reliable distance indicators at the 5% precision level or better. On the other hand, the two methods used to estimate the distance of the fast-declining SN 2006mr both yield a distance to NGC 1316 which is 25-30% larger. This disparity casts doubt on the suitability of fast-declining events for estimating extragalactic distances. Modest-to-negligible host galaxy reddening values are derived for all four supernovae. Nevertheless, two of them (SN 2006dd and SN 2006mr) show strong NaID interstellar lines in the host galaxy system. The strength of this absorption is completely inconsistent with the small reddening values derived from the supernova light curves if the gas in NGC 1316 is typical of that found in the interstellar medium of the Milky Way. In addition, the equivalent width of the NaID lines in SN 2006dd appear to have weakened significantly some 100-150 days after explosion. ; Comment: 50 pages, 13 figures, 10 tables; constructive comments welcome. Accepted for publication in AJ