We present results of one-dimensional theoretical models of photodissociation regions (PDRs), the predominantly neutral outer layers of molecular clouds exposed to an external far-ultraviolet (FUV) (6 eV < hv < 13.6 eV) radiation field. The models solve the chemical and thermal balance in the gas, and predict the emission from these regions primarily as a function of the incident FUV flux G0 (measured in units of 1.6 x 10(-3) ergs cm-2 s-1) and of the density n0 of the cloud. This paper extends previous work by Tielens and Hollenbach to lower densities and lower FUV fluxes by examining the parameter space 10(2) cm-3 < n0 less-than-or-equal-to 10(5) cm-3 and 1 less-than-or-equal-to G0 less-than-or-equal-to 10(4), relevant to molecular clouds in the ambient interstellar radiation field, reflection nebulae, and bright-rimmed clouds. This range is also relevant to observations of galaxies, where large ensembles of clouds 146-mu-m, [C I] 370 and 609-mu-m, [Si II] 35-mu-m, and [Fe II] 26 and 35-mu-m; the molecular rotational transitions (CO)-C-12 J = 1-0 and H-2 0-0 S(0); and the dust continuum intensities at 60 and 100-mu-m. In addition, we estimate the column density of FUV-pumped vibrationally excited H-2. The structure of a standard PDR (n0 = 10(3) cm-3, G0 = 10(3) cm-3) has a surface layer of A(nu) less-than-or-similar-to 1-2 mag of H, O, and C+ with a transition to H-2 and to C at A(v) greater-than-or-similar-to 1-2. Carbon is mostly CO at A(nu) greater-than-or-similar-to 4-6, and the oxygen not tied up in CO remains atomic to A(nu) approximately 10. The column density of atomic carbon, N(C), is of order 10(18) cm-2, relatively independent of n0 and G0. Hence, the intensities of the [C I] 370 and 609-mu-m lines are relatively insensitive to the physical parameters, and we ascribe their observed emission as arising from the PDR gas. Photoelectric heating dominates for A(nu) less-than-or-similar-to 6, and the cooling mostly emerges as [C II] 158-mu-m, with [O I] 63-mu-m also quite strong. Typically, the luminosity in [C II] 158-mu-m + [O I] 63-mu-m is of order 10(-3) to 10(-2) of the grain IR luminosity, a fraction which represents the efficiency of the photoelectric heating mechanism. We discuss the contribution of polycyclic aromatic hydrocarbons to photoelectric heating and conclude that the contribution is probably minor relative to the larger grains. We plot the ratio of the (CO)-C-12 J = 1-0 emission to the grain 100-mu-m intensity as a function of n0 and G0 and show that the ratio is sensitive to the FUV flux for G0 greater-than-or-similar-to 10.