The first moderate-resolution (FWHM approximately 100 eV) X-ray spectrum of a Seyfert 2 galaxy was obtained with the BBXRT experiment aboard Astro-1, The observed X-ray continuum of NGC 1068 from 0.3 to 10 keV is well fitted as the sum of two power-law spectra with no evidence for absorption intrinsic to the source. Strong Fe K emission lines with a total equivalent width of 2700 eV were detected due to iron less ionized than Fe xx and to iron more ionized than Fe XXIII. Unresolved Fe L lines with a total equivalent width of 340 eV were also seen. No evidence was seen for lines due to the recombination of highly ionized oxygen with an upper limit for the O Lyalpha emission line of 40 eV. The discovery of multiple Fe K and Fe L emission lines clearly indicates a broad range of ionization states for this gas. The X-ray emission from NGC 1068 is thought to be due to radiation from the obscured nucleus of the galaxy that is Compton-scattered by warm (T approximately 2 x 10(5) K) electrons above the obscuring material. We associate the cooler, less ionized Fe with the warm electrons producing the polarized optical light, and the hotter (T approximately 4 x 10(6) K), highly ionized Fe with a previously unseen component. The two components may share the same volume, or the hot component may be located closer to the nucleus. The X-ray emission from the two components is modeled for various geometries using a photoionization code that calculates the temperature and ionization state of the gas. We present models consistent with the X-ray, UV, and optical observations. Typical model parameters are a total Compton depth of a few percent, an inner boundary of the hot component of about 1 pc, and an inner boundary of the warm component of about 20 pc. All the successful models require that oxygen be underabundant compared with solar by a factor of at least 5, while Fe is most likely overabundant. We show that the observed optical and UV line strengths from the NLR are consistent with these abundances.