  [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.
