  We present in detail the implementation of the Blaizot-M\'endez-Wschebor
(BMW) approximation scheme of the nonperturbative renormalization group, which
allows for the computation of the full momentum dependence of correlation
functions. We discuss its signification and its relation with other schemes, in
particular the derivative expansion. Quantitative results are presented for the
testground of scalar O(N) theories. Besides critical exponents which are
zero-momentum quantities, we compute in three dimensions in the whole momentum
range the two-point function at criticality and, in the high temperature phase,
the universal structure factor. In all cases, we find very good agreement with
the best existing results.
