The gamma-ray astronomical observatory INTEGRAL, succesfully launched on 17 October 2002, carries two large gamma-ray telescopes. One of them is the coded-mask imaging gamma-ray telescope onboard the INTEGRAL satellite (IBIS) which provides high-resolution (≈ 12′) sky images of 29◦ × 29◦ in the energy range from 15 keV to 10 MeV with typical on-axis sensitivity of ≈ 1 mCrab at 100 keV (3σ, 10 s exposure). We report here the general description of the IBIS coded-mask imaging system and of the standard IBIS science data analysis procedures. These procedures reconstruct, clean and combine IBIS sky images providing at the same time detection, identification and preliminary analysis of point-like sources present in the field. Spectral extraction has also been implemented and is based on simultaneous fitting of source and background shadowgram models to detector images. The procedures are illustrated using some of the IBIS data collected during the inflight calibrations and present performance is discussed. The analysis programs described here have been integrated as instrument specific software in the Integral Science Data Center (ISDC) analysis software packages currently used for the Quick Look, Standard and Off-line Scientific Analysis.