  The redshifted 21-cm monopole is expected to be a powerful probe of the epoch
of the first stars and galaxies ($10<z<35$). The global 21-cm signal is
sensitive to the thermal and ionization state of hydrogen gas and thus provides
a tracer of sources of energetic photons -- primarily hot stars and accreting
black holes -- which ionize and heat the high redshift intergalactic medium
(IGM). This paper presents a strategy for observations of the global spectrum
with a realizable instrument placed in a low altitude lunar orbit, performing
night-time 40-120 MHz spectral observations, while on the farside to avoid
terrestrial radio frequency interference, ionospheric corruption, and solar
radio emissions. The frequency structure, uniformity over large scales, and
unpolarized state of the redshifted 21-cm spectrum are distinct from the
spectrally featureless, spatially-varying, and polarized emission from the
bright foregrounds. This allows a clean separation between the primordial
signal and foregrounds. For signal extraction, we model the foreground,
instrument, and 21-cm spectrum with eigenmodes calculated via Singular Value
Decomposition analyses. Using a Markov Chain Monte Carlo algorithm to explore
the parameter space defined by the coefficients associated with these modes, we
illustrate how the spectrum can be measured and how astrophysical parameters
(e.g., IGM properties, first star characteristics) can be constrained in the
presence of foregrounds using the Dark Ages Radio Explorer (DARE).
