A method for studying the star formation history (SFH) of nearby galaxies, as a function of time, has been developped and implemented. For the first time, the full SFH of a nearby dwarf irregular galaxy (DIG) has been retrieved from the photometry of its resolved stars. In the [(V-I),I] colour-magnitude diagram (CMD) of about 18000 stars in NGC 6822, two structures, the red-tangle and the red-tail, are the locus of the old and intermediate-age RGB and AGB stars. The tool used to retrieve the SFH is the comparison of the observed CMD with a set of model CMDs, computed assuming different evolutionary scenarios. The model CMDs have been computed in collaboration with the Padova Group if stellar evolution. Their reliability is a result of three main components : i) a reliable set of stellar evolutionary models covering the needed range of ages and metallicities, ii) the interpolation of the stellar evolutionary tracks of fixed mass and metallicity to determine the smooth distribution of stars of any age, mass, and metallicity on the CMD, and iii) a realistic simulation of the observational effects on the synthetic CMD. The following constraints have been put on the SFH of NGC 6822: --Star formation beginning in NGC 6822 at T_i<= 6 Gyr can be ruled out. It has most likely begun at a very early epoch (about 15-12 Gyr ago), from low metallicity gas. --An SFR close to constant or declining in the last few Gyr of the galaxy's lifetime seems best to reproduce the observations. -- An overall enhancement of the star formation activity has occurred in the last 100-200 Myr. The strength of this enhancement has been different in different regions of the galaxy. The fundamentals of the method can be applied to galaxies of any morphological type, provided that deep enough photometry is available. This can be achieved, from the ground, for all Local Group galaxies, and using HST, for galaxies within 4--5 Mpc.