  We present the results of spectroscopic observations of targets discovered
during the first two years of the ESSENCE project. The goal of ESSENCE is to
use a sample of ~200 Type Ia supernovae (SNe Ia) at moderate redshifts (0.2 < z
< 0.8) to place constraints on the equation of state of the Universe.
Spectroscopy not only provides the redshifts of the objects, but also confirms
that some of the discoveries are indeed SNe Ia. This confirmation is critical
to the project, as techniques developed to determine luminosity distances to
SNe Ia depend upon the knowledge that the objects at high redshift are the same
as the ones at low redshift. We describe the methods of target selection and
prioritization, the telescopes and detectors, and the software used to identify
objects. The redshifts deduced from spectral matching of high-redshift SNe Ia
with low-redshift SNe Ia are consistent with those determined from host-galaxy
spectra. We show that the high-redshift SNe Ia match well with low-redshift
templates. We include all spectra obtained by the ESSENCE project, including 52
SNe Ia, 5 core-collapse SNe, 12 active galactic nuclei, 19 galaxies, 4 possibly
variable stars, and 16 objects with uncertain identifications.
