The property of dark energy and the physical reason for the acceleration of the present universe are two of the most difficult problems in modern cosmology. The dark energy contributes about two-thirds of the critical density of the present universe from the observations of type-Ia supernovae (SNe Ia) and anisotropy of cosmic microwave background (CMB). The SN Ia observations also suggest that the universe expanded from a deceleration to an acceleration phase at some redshift, implying the existence of a nearly uniform component of dark energy with negative pressure. We use the "Gold" sample containing 157 SNe Ia and two recent well-measured additions, SNe Ia 1994ae and 1998aq to explore the properties of dark energy and the transition redshift. For a flat universe with the cosmological constant,we measure ΩM = 0.28+0.04 -0.05,which is consistent with Riess et al. The transition redshift is zT=0.60+0.06 -0.08. We also discuss several dark energy models that define w(z) of the parameterized equation of state of dark energy including one parameter and two parameters (w(z) being the ratio of the pressure to energy density). Our calculations show that the accurately calculated transition redshift varies from zT=0.06+0.07 -0.06 to zT=0.06+0.06 -0.08 across these models. We also calculate the minimum redshift zc at which the current observations need the universe to accelerate.