We present a detailed analysis of the distance determination for one Intermediate Velocity Cloud ( IVC \mathrm { G } 139.6 + 47.6 ) from the ongoing DDO IVC Distance Project . Stars along the line of sight to \mathrm { G } 139.6 + 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 \pm 10 pc for the lower limit and 257 ^ { +211 } _ { -33 } 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 .