A detailed study of the star formation history of the Sagittarius dwarf spheroidal galaxy is performed through the analysis of data from the Sagittarius Dwarf Galaxy Survey (SDGS). Accurate statistical decontamination of the SDGS colour-magnitude diagrams (CMDs) allows us to obtain many useful constraints on the age and metal content of the Sgr stellar populations in three different regions of the galaxy. A coarse metallicity distribution of Sgr stars is derived, ranging from [Fe/H] similar to -2.0 to [Fe/H] similar to -0.7, the upper limit being somewhat higher in the central region of the galaxy. A qualitative global fit to all the observed CMD features is attempted, and a general scheme for the star formation history of the Sgr dSph is derived. According to this scheme, star formation began at a very early time from a low metal content interstellar medium and lasted for several Gyr, coupled with progressive chemical enrichment. The star formation rate (SFR) had a peak from 8 to 10 Gyr ago, when the mean metallicity was in the range -1.3 less than or equal to [Fe/H] less than or equal to -0.7. After that maximum, the SFR rapidly decreased and a very low rate of star formation took place until similar to 1-0.5 Gyr ago.