We describe and apply the methods that have been developed to calibrate the Advanced Stokes Polarimeter and to compensate for the polarization effects introduced by the Vacuum Tower Telescope at the National Solar Observatory/Sunspot. A seven-parameter model of the telescope is fitted to data obtained at a variety of mirror angles using observations of both the center of the solar disk and that point within a sunspot umbra at which the magnetic field is oriented as close to the line of sight as possible. The response matrix of the polarimeter itself is determined by the use of polarizing calibration optics that modify the polarization state of the beam exiting the telescope but before entering the polarimeter. A global least-squares solution is obtained simultaneously for the response matrix and the telescope parameters. A detailed gain-correction procedure is described that reduces the multiplicative gain errors in the spectral images to typically less than 1%. We have successfully recovered net-linear polarization profiles with peak amplitudes of 1 x 10-3Ic against an instrumentally produced background polarization of ~=1--5 x 10-2Ic. Net-polarization signals smaller than ~=3 x 10-4Ic are lost, even with sufficient averaging, in a background due to photometric and other calibration errors.