We perform extensive simulations of a two-dimensional Lennard-Jones glass subjected to quasistatic shear deformation at T=0 . We analyze the distribution of nonaffine displacements in terms of contributions of plastic, irreversible events, and elastic, reversible motions. From this, we extract information about correlations between plastic events and about the elastic nonaffine noise. Moreover, we find that nonaffine motion is essentially diffusive, with a clearly size-dependent diffusion constant. These results, supplemented by close inspection of the evolving patterns of the nonaffine tangent displacement field, lead us to propose a phenomenology of plasticity in such amorphous media. It can be schematized in terms of elastic loading and irreversible flips of small, randomly located shear transformation zones, elastically coupled via their quadrupolar fields.