  We are presenting in this paper a detailed account of the methods used to
compute the three-dimensional two-point galaxy correlation function in the
VIMOS-VLT deep survey (VVDS). We investigate how instrumental selection effects
and observational biases affect the measurements and identify the methods to
correct them. We quantify the accuracy of our correction method using an
ensemble of fifty mock galaxy surveys generated with the GalICS semi-analytic
model of galaxy formation which incorporate the same selection biases and
tiling strategy as the real data does. We demonstrate that we are able to
recover the real-space two-point correlation function xi(s) to an accuracy
better than 10% on scales larger than 1 h^{-1} Mpc, and of about 30% on scales
below 1 h^{-1} Mpc, with the sampling strategy used for the first epoch VVDS
data. The projected correlation function w_p(r_p) is recovered with an accuracy
better than 10% on all scales 0.1 <= r <= 10 h^{-1} Mpc. There is a tendency
for a small but systematic under-estimate of the correlation length derived
from w_p(r_p) of 6% on average, remaining after our correction process. The
large number of simulated surveys allows us to provide a reliable estimate of
the cosmic error on the measurements of the correlation length r_0, of about
15-20% for the first epoch VVDS observation (Le Fevre et al.2004,
astro-ph/0409133). The error estimation and measurement techniques outlined in
this paper are being used in several studies which investigate in detail the
clustering properties of galaxies in the VVDS data.
