Spectroscopy for the Investigation of the Characteristics of the Atmosphere of Mars (SPICAM) is the first instrument orbiting a planet other than Earth that is dedicated to the technique of stellar occultation. During the first year of operation on board Mars Express, SPICAM observed more than 500 star occultations, yielding vertical profiles of CO2, ozone, and dust/clouds/aerosols. We review the principles of a star occultation in the absorptive regime, emphasizing two advantages of this method: an absolute value is obtained from a relative measurement without the need for an absolute calibration of the instrument, and the altitude of the measurement is accurately known because it depends only on the position of the spacecraft and not on the pointing of the instrument. We describe a general algorithm used for all occultations. First, we derive from the raw data the transmission of the atmosphere as a function of wavelength, T(λ, z), taking account of instrument-specific factors. Then a spectral inversion retrieves the slant densities (local densities integrated along the line of sight) of all absorbing species for each measurement of the transmission T(λ, z) during the occultation. Finally, a vertical inversion retrieves the vertical distribution of the local densities from the series of the slant density measurements. This vertical inversion includes a new scheme of Tikhonov regularization. This paper will serve as a reference for the SPICAM Mars Express data which will be systematically made available to the public in the PDS-like archive managed by ESA.