The Thirty Meter Telescope (TMT) with its first-light multi-conjugate adaptive optics system, NFIRAOS, and high-resolution imager, IRIS, is expected to take differential astrometric measurements with an accuracy on the order of tens of micro arcsec. This requires the control, correction, characterization and calibration of a large number of error sources and uncertainties, many of which have magnitudes much in excess of this level of accuracy. In addition to designing the observatory such that very high precision and accuracy astrometric observations are enabled, satisfying the TMT requirements can only be achieved by a careful calibration, observation and data reduction strategy. In this paper, we present descriptions of the individual errors sources, how and when they apply to different astrometry science cases and the mitigation methods required for each of them, as well as example results for individual error terms and the overall error budgets for a variety of different science cases.