We present three methods for deriving the velocity field in magnetized regions of the Sun's photosphere. As a preliminary step, we introduce a Fourier-based local correlation tracking (LCT) routine that we term "FLCT." By explicitly employing the observation made by Démoulin & Berger, that results determined by LCT applied to magnetograms involve a combination of all components of the velocity and magnetic fields, we show that a three-component velocity field can be derived, in a method we term algebraic decomposition, or ADC. Finally, we introduce ILCT, a method that enforces consistency between the normal component of the induction equation and results obtained from LCT. When used with photospheric vector magnetograms, ILCT determines a three-component photospheric velocity field suitable for use with time sequences of such magnetograms to drive boundary conditions for MHD simulations of the solar corona. We present results from these methods applied to vector magnetograms of NOAA AR 8210 on 1998 May 1.