  The pulsar velocity distribution provides information about the binary
history of pulsar progenitors as well as asymmetries of the supernova events in
which pulsars are born. Studies of local pulsars present a biased view of this
distribution, since they preferentially select low velocity pulsars that have
remained near their birthplaces in the Galactic plane. Using the VLA, we have
studied the proper motions of a large sample of distant pulsars. These pulsars
are generally faint, and the expected proper motions are small. In this paper,
we describe the data analysis techniques that we have developed to allow
precise astrometric measurements of faint sources with the VLA. These
techniques include ``gating'' the VLA correlator to increase the
signal-to-noise ratio of the pulsar by gathering data only during the pulse.
Wide-field imaging techniques, including multiband imaging to account for
bandwidth smearing, were used to allow identification of multiple in-beam
background sources for astrometric calibration. We present the analysis of
three pulsars, and demonstrate that astrometric accuracy of about ten
milliarcseconds can be obtained for individual sources with our technique,
allowing measurement of proper motions with errors of only a few
milliarcseconds per year over our seven year baseline.
