We present a comprehensive and self-consistent empirical model for several plasma parameters in the extended solar corona above a polar coronal hole. The model is derived from observations with the SOHO Ultraviolet Coronagraph Spectrometer (UVCS/SOHO) during the period between 1996 November and 1997 April. We compare observations of H I Lyα and O VI λλ1032, 1037 emission lines with detailed three-dimensional models of the plasma parameters and iterate for optimal consistency between measured and synthesized observable quantities. Empirical constraints are obtained for the radial and latitudinal distribution of density for electrons, H0, and O5+, as well as the outflow velocity and unresolved anisotropic most probable speeds for H0 and O5+. The electron density measured by UVCS/SOHO is consistent with previous solar minimum determinations of the white-light coronal structure; we also perform a statistical analysis of the distribution of polar plumes using a long time series. From the emission lines we find that the unexpectedly large line widths of H0 atoms and O5+ ions at most heights are the result of anisotropic velocity distributions. These distributions are not consistent with purely thermal motions or the expected motions from a combination of thermal and transverse wave velocities. Above 2 R☉, the observed transverse most probable speeds for O5+ are significantly larger than the corresponding motions for H0, and the outflow velocities of O5+ are also significantly larger than the corresponding velocities of H0. Also, the latitudinal dependence of intensity constrains the geometry of the wind velocity vectors, and superradial expansion is more consistent with observations than radial flow. We discuss the constraints and implications on various theoretical models of coronal heating and acceleration.