ASASSN-14li is a recently discovered tidal disruption event with an exceptionally rich data set: spectra and lightcurves in soft X-rays, UV, optical, and radio. To understand its emission properties in all these bands, we have extended our model for post-tidal disruption accretion and photon production to estimate both soft X-ray radiation produced by the "prompt" accretion phase and synchrotron emission associated with the bow shock driven through an external medium by the unbound tidal debris, as well as optical and UV light. We find that fiducial values of the stellar mass () and black hole mass () yield quantitative agreement with the optical/UV luminosity, lightcurve, and color temperature; approximate agreement with the soft X-ray spectrum and lightcurve; and quantitative agreement with the radio luminosity, spectrum, and lightcurve. Equipartition analysis of the radio data implies that the radio-emitting region expands with a constant speed, and its magnitude is comparable to the speed expected for the unbound stellar ejecta. Both facts provide strong support to our model. We find that the disruption event took place in 2014 mid-September. Two independent parameters, the magnitude and logarithmic radial gradient of the ambient gas density near the black hole, must be fit to the data to explain the radio emission; their inferred values are comparable to those found near both Sgr A* and the TDE candidate Swift J1644.