[Abridged] We present a homogeneous and complete catalogue of optical groups identified in the purely flux limited (17.5<=I<=24.0) VIMOS-VLT Deep Survey (VVDS). We use mock catalogues extracted from the MILLENNIUM simulation, to correct for potential systematics that might affect the overall distribution as well as the individual properties of the identified systems. Simulated samples allow us to forecast the number and properties of groups that can be potentially found in a survey with VVDS-like selection functions. We use them to correct for the expected incompleteness and also to asses how well galaxy redshifts trace the line-of-sight velocity dispersion of the underlying mass overdensity. In particular, we train on these mock catalogues the adopted group-finding technique (the Voronoi-Delaunay Method, VDM). The goal is to fine-tune its free parameters, recover in a robust and unbiased way the redshift and velocity dispersion distributions of groups and maximize the level of completeness (C) and purity (P) of the group catalogue. We identify 318 VVDS groups with at least 2 members within 0.2<=z<=1.0, among which 144 (/30) with at least 3 (/5) members. The sample has globally C=60% and P=50%. Nearly 45% of the groups with at least 3 members are still recovered if we run the algorithm with a parameter set which maximizes P (75%). We exploit the group sample to study the redshift evolution of the fraction f_b of blue galaxies (U-B<=1) within 0.2<=z<=1. We find that f_b is significantly lower in groups than in the whole ensemble of galaxies irrespectively of their environment. These quantities increase with redshift, with f_b in groups showing a marginally significant steeper increase. We also confirm that, at any explored redshift, f_b decreases for increasing group richness, and we extend towards fainter luminosities the magnitude range over which this result holds. Comment: Submitted to A&A, revised version after referee comments, Table 5 added