We present theoretical models of the time-dependent thermal and chemical structure of molecular gas suddenly exposed to far-ultraviolet (FUV) (6 eV less than hv less than 13.6 eV) radiation fields and the consequent time- dependent infrared emission of the gas. We focus on the response of molecular hydrogen for cloud densities ranging from n = 10(exp 3) to 10(exp 6)/cu cm and FUV fluxes G(sub 0) = 10(exp 3)-10(exp 6) times the local FUV interstellar flux. For G(sub 0)/n greater than 10(exp -2) cu cm, the emergent H(sub 2) vibrational line intensities are initially larger than the final equilibrium values. The H(sub 2) lines are excited by FUV fluorescence and by collisional excitation in warm gas. Most of the H(sub 2) intensity is generated at a characteristic hydrogen column density of N approximately 10(exp 21)/sq cm, which corresponds to an FUV optical depth of unity caused by dust opacity. The time dependence of the H(sub 2) intensities arises because the initial abundances of H(sub 2) at these depths is much higher than the equilibrium values, so that H(sub 2) initially competes more effectively with dust in absorbing FUV photons. Considerable column densities of warm (T approximately 1000) K H(sub 2) gas can be produced by the FUV pumping of H(sub 2) vibrational levels followed by collisional de-excitation, which transfers the energy to heat. In dense (n greater than or approximately 10(exp 5)/cu cm) gas exposed to high (G(sub 0) greater than or approximately 10(exp 4)) fluxes, this warm gas produces a 2-1 S(1)/1-0 S(l) H(sub 2) line ratio of approximately 0.1, which mimics the ratio found in shocked gas. In lower density regions, the FUV pumping produces a pure-fluorescent ratio of approximately 0.5. We also present calculations of the time dependence of the atomic hydrogen column densities and of the intensities of 0 I 6300 A, S II 6730 A, Fe II 1.64 microns, and rotational OH and H20 emission. Potential applications include star-forming regions, clouds near active galactic nuclei, and planetary nebulae. We apply our models to five planetary nebulae and conclude that only BD +30deg3639 shows evidence of enhanced H(sub 2) emission due to (high) nonequilibrium H(sub 2) abundances.