This paper provides a description of the Space Telescope (ST) Pointing System (PS), and an overview of the pointing operations and procedures that support celestial observations. It is aimed at indicating to the user-astronomer the ST pointing capabilities and the mechanics of insuring the presence of the correct star in an instrument aperture. The paper begins by summarizing the general requirements regarding image stability and pointing accuracy to which the ST is being designed. This is followed by a description of the PS, in which primary elements are rate gyros, star sensors, reaction wheels, and an onboard digital computer. The Fine Guidance System is the star sensor that provides the precise, long term celestial reference and is given special emphasis, since its autonomous modes are so intimately tied to the acquisition process. A description of a nominal acquisition sequence is given, and some strategies for dealing with acquisition and pointing anomalies are discussed.