We describe the observing strategy, data reduction tools, and early results of a supernova (SN) search project, named SUDARE, conducted with the ESO VST telescope, which is aimed at measuring the rate of the different types of SNe in the redshift range 0.2 < z < 0.8. The search was performed in two of the best studied extragalactic fields, C DFS and C OSMOS, for which a wealth of ancillary data are available in the literature or in public archives. To accurately characterize the surveyed stellar population, we exploit public data and our own observations to measure the galaxy photometric redshifts and rest frame colours. The dispersion of the rate measurements for SNe-Ia is comparable to the scatter of the theoretical tracks for single degenerate (SD) and double degenerate (DD) binary systems models, therefore it is not possible to disentangle among the two different progenitor scenarios. Unlike recent claims, the core collapse SN rate is fully consistent with the prediction that is based on recent estimates of star formation history and standard progenitor mass range.