We present new results from the analysis of 55 high-resolution spectra of V404 Cyg (the optical counterpart of the X-ray transient GS 2023+338) taken in 1991 July-August which, added to our 1990 July Hα spectra, establish the most complete spectroscopic data base in quiescence of this new black hole candidate. In addition, we present multicolour (optical and infrared) and white-light photometry, the latter being partially simultaneous with the spectroscopy. We detect V404 Cyg B through its metallic absorption lines in the vicinity of Ha, which classify it as a KO(±1) III-V star. The absorption lines are partially filled in by a flat continuum, probably an accretion disc, which contributes < 10 per cent of the total flux in R. Short-time-scale (˜hours) variations in the 1990 continuum and the Ha profile are superposed on a smooth orbital modulation. The photometric variations on the orbital period are consistent with the ellipsoidal effect, whereas the profile changes can be interpreted as the orbital motion associated with the hotspot/ gas stream. The presence of intense narrow Ha components at the radial velocity of the secondary star suggests heating of its inner face. The Balmer decrement is consistent with recombination case B, and therefore the emission lines are optically thin and produced by photoionization. Photometric colours indicate that the interstellar extinction has hitherto been underestimated, and we propose a new value of AV˜4.0. This result, as well as the requirement that the secondary fills its Roche lobe, rules out a main-sequence classification for the companion star and supports a luminosity class of III or W The subgiant spectral type is the most likely classification in terms of the distance and implied peak LX. In addition, the observed widths of the metallic lines allow us to set a limit of <35 km s-1 to the rotational broadening of V404 Cyg B, which constrains the mass ratio q to be <0.04 for a Roche-lobe-filling secondary. The amplitude of the ellipsoidal modulation and the very narrow emission lines suggest a low-inclination system (i≤40°). We also find evidence for the previously reported 0.24-d modulation in both the Hα emission radial velocities and the photometry. The origin of this modulation, however, remains obscure.