An analysis of numerous homogenized UBV photoelectric observations and red spectra of the Be star V832 Cyg from several observatories led to the following principal findings: 1. Pronounced long-term light and colour variations of V832 Cyg result from a combination of two effects: from the gradual formation of a new Be envelope, and from an asymmetry and a slow revolution of the envelope (or its one-armed oscillation). The colour variations associated with the envelope formation are characterized by a positive correlation between brightness and emission strength, typical for stars which are not seen roughly equator-on. 2. The V magnitude observations prewhitened for the long-term changes follow a sinusoidal orbital light curve with a small amplitude and a period of 28.1971d which is derived from observations spanning 43 years. This independently confirms a 12-year old suggestion that the star is a spectroscopic binary with a 29-d period. V832 Cyg thus becomes the fifth known Be star with cyclic long-term V/R variations, the duplicity of which has been proven, the four other cases being ζ Tau, V923 Aql, γ Cas and X Per. Therefore, the hypothesis that the long-term V/R variations may arise due to the attractive force of the binary companion at certain phases of the envelope formation is still worth considering as a viable alternative to the model of one-armed oscillation. 3. We have shown that the RV and V/R variations of the Hα and He I 6678 emission lines are all roughly in phase. In particular, the He I 6678 emission also moves with the Be primary which differs from what was found for another Be binary, \varphi Per. 4. We derived the orbital elements and found that in spite of the remaining uncertainties, the basic physical properties of the 28.2d binary are well constrained. 5. The light minimum of the orbital light curve occurs at elongation when the Be star is approaching us and the object becomes bluest in (B-V) and reddest in (U-B) at the same time. This may indicate that a part of the optically thick regions of the envelope is eclipsed at these orbital phases. Guest investigator, Dominion Astrophysical Observatory, Herzberg Institute of Astrophysics, National Research Council of Canada. Also based on observations from Castanet-Tolosan, Hvar, Ondrejov, Pic-du-Midi, Rozen, San Pedro Martir, Toronto and Xing-Long Observatories and on photoelectric photometry by AAVSO members. Tables 3, 5-7 are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/387/580};