ASTEP South is the first phase of the ASTEP project (Antarctic Search for Transiting ExoPlanets). The instrument is a fixed 10 cm refractor with a 4kx4k CCD camera in a thermalized box, pointing continuously a 3.88 degree x 3.88 degree field of view centered on the celestial South pole. ASTEP South became fully functional in June 2008 and obtained 1592 hours of data during the 2008 Antarctic winter. The data are of good quality but the analysis has to account for changes in the point spread function due to rapid ground seeing variations and instrumental effects. The pointing direction is stable within 10 arcseconds on a daily timescale and drifts by only 34 arcseconds in 50 days. A truly continuous photometry of bright stars is possible in June (the noon sky background peaks at a magnitude R=15 arcsec-2 on June 22), but becomes challenging in July (the noon sky background magnitude is R=12.5 arcsec?2 on July 20). The weather conditions are estimated from the number of stars detected in the field. For the 2008 winter, the statistics are between 56.3 % and 68.4 % of excellent weather, 17.9 % to 30 % of veiled weather and 13.7 % of bad weather. Using these results in a probabilistic analysis of transit detection, we show that the detection efficiency of transiting exoplanets in one given field is improved at Dome C compared to a temperate site such as La Silla. For example we estimate that a year-long campaign of 10 cm refractor could reach an efficiency of 69 % at Dome C versus 45 % at La Silla for detecting 2-day period giant planets around target stars from magnitude 10 to 15. This shows the high potential of Dome C for photometry and future planet discoveries. [Short abstract]