Energy sources for the strong emission lines and far-infrared emission in NGC 6240 have been examined using optical imaging, long-slit spectra, and fiber-array area spectroscopy. The strong optical line emission appears to result mainly from shocks between clouds with large chaotic motions. An active nucleus has been identified via extended regions showing weak, broad emission at Hα, interpreted as light from a Seyfert nucleus seen via scattering from dust. The spectral energy distributions of the two central light concentrations are quite similar, strengthening the case for their being remnant nuclei of merging galaxies. Optical evidence indicates a moderate amount of star formation; H II regions are seen only outside the nuclear region, and do not contribute a significant fraction of the emission-line luminosity. Continuum colors suggest substantial past star formation near the strongest dust lane and in tidal tails. Energy-balance arguments indicate that "cirrus" emission (from dust heated by the absorption of optical radiation from the overall stellar population) is an important contributor to the total far-infrared flux. Such emission is relatively strong in this system because the disturbed dust distribution is more effective at absorbing visible-wavelength starlight than in a normal spiral, as can be shown from color and spatially filtered images. In addition, the optically derived velocity field suggests that much of the dust heating may be due to shocks associated with the merging systems and the optical emission-line region. If the ionized gas represents less than about 10-4 of the total gas content, the energy stored in gas motions is sufficient to power the observed luminosity of NGC 6240 for 107 yr, in which case starbursts need have only a minor role in the energetics of such systems.