  The presence of dark energy in the Universe is inferred directly from the
accelerated expansion of the Universe, and indirectly, from measurements of
cosmic microwave background (CMB) anisotropy. Dark energy contributes about 2/3
of the critical density, is very smoothly distributed, and has large negative
pressure. Its nature is very much unknown. Most of its discernible consequences
follow from its effect on evolution of the expansion rate of the Universe,
which in turn affects the growth of density perturbations and the age of the
Universe, and can be probed by the classical kinematic cosmological tests.
Absent a compelling theoretical model (or even a class of models), we describe
dark energy by an effective equation of state w=p_X/rho_X which is allowed to
vary with time. We describe and compare different approaches for determining
w(t), including magnitude-redshift (Hubble) diagram, number counts of galaxies
and clusters, and CMB anisotropy, focusing particular attention on the use of a
sample of several thousand type Ia supernova with redshifts z < 1.7, as might
be gathered by the proposed SNAP satellite. Among other things, we derive
optimal strategies for constraining cosmological parameters using type Ia
supernovae. While in the near term CMB anisotropy will provide the first
measurements of w, supernovae and number counts appear to have the most
potential to probe dark energy.
