The model-independent method of using type Ia supernovae proposed and developed by Daly & Djorgovski (2003, 2004) has been applied to the Riess et al. (2007) supernovae sample. Assuming only a Robertson-Walker metric, we find q 0=-0.5±0.13, indicating that the universe is accelerating today. This result is purely kinematic, is independent of the contents of the universe, and does not require that a theory of gravity be specified. Our model-independent method allows a determination of q(z) for a particular value of space curvature. When q(z) transitions from negative to positive values, the universe transitions from an accelerating to a decelerating state. For zero space curvature, we find that the universe transitions from acceleration to deceleration at a zedshift of about z T=0.35 -0.7 +0.15 for the Riess et al. (2007) sample. If a theory of gravity is specified, the supernovae data can be used to determine the pressure, energy density, and equation of state of the dark energy, and the potential and kinetic energy density of a dark energy scalar field as functions of redshift. The relevant equations from General Relativity are applied, and these functions are obtained. The results are consistent with predictions in the standard Lambda Cold Dark Matter model at about the two sigma level.