The unique advantages for astronomy on the Antarctic plateau are now well established. In particular, Dome C, Antarctica is potentially one of the best new sites for optical, infrared and sub-millimeter astronomy, presenting the opportunity to build unique astronomical instruments. Located high on the Antarctic plateau, Dome C offers low wind, clear skies, and negligible precipitation. This thesis addresses three additional properties of the site relevant to optical astronomy-sky brightness, atmospheric extinction and optical turbulence. The sky at an optical astronomy site must be dark, and the atmosphere very clean with minimal light extinction. At present little is known from an astronomer's perspective about the optical sky brightness and atmospheric extinction at most Antarctic sites. The high latitude of Dome C means that the Sun spends a relatively small amount of time far below the horizon, implying longer periods of astronomical twilight and less optical dark time than other sites, especially those close to the equator. We review the contributions to sky brightness at high-latitude sites, and calculate the amount of usable dark time at Dome C. We also explore the implications of the limited sky coverage of high-latitude sites, and review optical extinction data from the South Pole. A proposal to extend the amount of usable dark time through the use of polarising filters is examined, and we present the design and calibration of an instrument (called Nigel) to measure the brightness, spectrum and temporal characteristics of the twilight and night sky. The atmospheric turbulence profile above an astronomical site limits the achievable resolution and sensitivity of a telescope. The atmospheric conditions above high plateau Antarctic sites are different to temperate sites; the boundary layer of turbulence is confined very close to the surface, and the upper atmosphere turbulence very weak. We present the first winter-time turbulence profiles of the atmosphere above Dome C, and characterise the site in terms of the achievable precision for photometry and astrometry, and the isoplanatic angle and coherence time for the adaptive optics.