The DDO IVC Distance Project: Survey Description and the Distance to G139.6+47.6

We present a detailed analysis of the distance determination for one intermediate Velocity Cloud (IVC G139.6+47.6) from the ongoing DDO IVC Distance Project. Stars along the line of sight to G139.6+47.6 are examined for the presence of sodium absorption attributable to the cloud, and the distance bracket is established by astrometric and spectroscopic parallax measurements of demonstrated foreground and background stars. We detail our strategy regarding target selection, observational setup, and analysis of the data, including a discussion of wavelength calibration and sky subtraction uncertainties. We find a distance estimate of 129 (+/- 10) pc for the lower limit and 257 (+211-33) pc for the upper limit. Given the high number of stars showing absorption due to this IVC, we also discuss the small-scale covering factor of the cloud and the likely significance of non-detections for subsequent observations of this and other similar IVC's. Distance measurements of the remaining targets in the DDO IVC project will be detailed in a companion paper.