The structure of the low temperature phase of NH₄MnF₃ has been determined by means of X-ray powder diffraction using the Rietveld method. The structure is orthorhombic with space group Pnma, Z=4. The unit cell dimensions at T=83 K are a=5.952(1) AA, b=8.541(1) AA and c=5.949(1) AA. The low temperature Raman spectra have been interpreted consistently with the space group. The librational modes of the ammonium ion have been identified from the temperature dependence of the Raman lines. A model for the orientations of the NH₄⁺ ions is proposed such that the minimum energy is achieved when each H atom points towards one of the four nearest F atoms. The depolarization of some of the Raman peaks in tentatively explained as an effect of orientational disorder of the NH₄⁺ ions in the low temperature phase.