THE Michigan/MIKE fiber system survey of stellar radial velocities in dwarf spheroidal galaxies: Acquisition and reduction of data

We introduce a stellar velocity survey of dwarf spheroidal galaxies, undertaken using the Michigan/MIKE Fiber System (MMFS) at the Magellan/Clay 6.5 m telescope at Las Campanas Observatory. As of 2006 November we have used MMFS to collect 6415 high-resolution (R = 20,000-25,000) spectra from 5180 stars in four dwarf spheroidal galaxies: Carina, Fornax, Sculptor, and Sextans. Spectra sample the range 5140-5180 Å, which includes the prominent magnesium triplet absorption feature. We measure radial velocity (RV) to a median precision of 2.0 km s^-1 for stars as faint as V ∼ 20.5. From the spectra we also are able to measure the strength of iron and magnesium absorption features using spectral indices that correlate with effective temperature, surface gravity, and chemical abundance. Measurement of line strength allows us to identify interloping foreground stars independently of velocity and to examine the metallicity distribution among dSph members. Here we present detailed descriptions of MMFS, our target selection and spectroscopic observations, the data reduction procedure, and error analysis. We compare our RV results to previously published measurements for individual stars. In some cases we find evidence for a mild, velocity-dependent offset between the RVs that we measure using the magnesium triplet and previously published RV measurements derived from the infrared calcium triplet. In companion papers we will present the complete data sets and kinematic analyses of these new observations.