The Goddard High Resolution Spectrograph (GHRS) has two square entrance apertures, one two arc seconds and the other one quarter arc second on a side. Light from the astronomical target must be focused onto one of them prior to beginning a spectroscopic observation. The acquisition process is initiated with the target in the large aperture, followed by a slew to center the target in the small aperture if desired. The GHRS software supports both observer interactive and autonomous on-board modes of target acquisition. Software exists which executes a search pattern by commanding slews of the spacecraft, makes high resolution maps of the field of view of either aperture, recognizes the presence of the desired object, measures its precise location within the aperture, computes and commands a centering maneuver, and measures the flux of light at the conclusion. For most of these functions there are several options or algorithms, providing the flexibility to support a wide range of brightness and spectral content, extended or point sources, isolated or crowded fields, stationary or moving targets. Most acquisitions will be performed in undispersed ultraviolet light, although the capability to image the target in the light of an individual emission line is under development.