A deep (~70%) and extended (~150 days) eclipse was seen towards the young multiple stellar system V773 Tau in 2010. We interpret it as due to the passage of a circumbinary disk around the B components moving in front of the A components. Our aim is to characterise the orientation and structure of the disk, to refine the orbits of the subcomponents, and to predict when the next eclipse will occur. We combine the photometry from several ground based surveys, construct a model for the light curve of the eclipse, and use high angular resolution imaging to refine the orbits of the three components of the system, A, B and C. Frequency analysis of the light curves, including from the TESS satellite, enables characterisation of the rotational periods of the Aa and Ab stars. A toy model of the circumbinary disk shows that it extends out to approximately 5 au around the B binary and has an inclination of 73 degrees with respect to the orbital plane of AB, where the lower bound of the radius of the disk is constrained by the geometry of the AB orbit and the upper bound is set by the stability of the disk. We identify several frequencies in the photometric data that we attribute to rotational modulation of the Aa and Ab stellar companions. We produce the first determination of the orbit of the more distant C component around the AB system and limit its inclination to 93 degrees. The high inclination and large diameter of the disk, together with the match from theory suggest that B is an almost equal mass, moderately eccentric binary. We identify the rotational periods of the Aa and Ab stars, identify a third frequency in the light curve that we attribute to the orbital period of the stars in the B binary. We predict that the next eclipse will be around 2037, during which both detailed photometric and spectroscopic monitoring will characterise the disk in greater detail.