  We present a multiplexed, high-resolution (R~50,000 median) spectroscopic
survey designed to detect exoplanet candidates in two southern star clusters
(NGC 2516 and NGC 2422) using the Michigan/Magellan Fiber System (M2FS) on the
Magellan/Clay telescope at Las Campanas Observatory. With 128 available fibers
in our observing mode, we are able to target every star in the core half-degree
of each cluster that could plausibly be a solar-analog member. Our
template-based spectral fits provide precise measurements of fundamental
stellar properties - $T_{eff}$ ($\pm$30 K), [Fe/H] and [$\alpha$/Fe] ($\pm$0.02
dex), and $v_r\sin(i)$ ($\pm$0.3 km/s) - and radial velocities (RVs) by using
telluric absorption features from 7160 to 7290 $\AA$ as a wavelength reference
for 251 mid-F to mid-K stars (126 in NGC 2516 and 125 in NGC 2422) that
comprise our survey. In each cluster we have obtained ~10-12 epochs of our
targets. Using repeat observations of an RV standard star we show our approach
can attain a single-epoch velocity precision of 25 m/s to 60 m/s over a broad
range of S/N throughout our observational baseline of 1.1 years. Our technique
is suitable for non-rapidly rotating stars cooler than mid-F. In this paper we
describe our observational sample, analysis methodology, and present a detailed
study of the attainable precision and measurement capabilities of our approach.
Subsequent papers will provide results for stars observed in the target
clusters, analyze our dataset of RV time-series for stellar jitter and stellar
and sub-stellar companions, and consider the implications of our findings on
the clusters themselves.
