  We report on our exploratory study for the direct evaluation of the parton
distribution functions from lattice QCD, based on a recently proposed new
approach. We present encouraging results using Nf = 2 + 1 + 1 twisted mass
fermions with a pion mass of about 370 MeV. The focus of this work is a
detailed description of the computation, including the lattice calculation, the
matching to an infinite momentum and the nucleon mass correction. In addition,
we test the effect of gauge link smearing in the operator to estimate the
influence of the Wilson line renormalization, which is yet to be done.
