The halo occupation distribution (HOD) describes the bias between galaxies and dark matter by specifying (a) the probability P(N|M) that a halo of virial mass M contains N galaxies of a particular class and (b) the relative distributions of galaxies and dark matter within halos. We calculate predicted HODs for a Lambda-CDM cosmological model using an SPH hydrodynamic simulation and a semi-analytic (SA) galaxy formation model. Although the two methods predict different galaxy mass functions, their HOD predictions agree remarkably well. For mass-selected samples, the mean occupation <N(M)> exhibits a sharp cutoff at low halo masses, a slowly rising plateau for <N>~1-2, and a more steeply rising high occupancy regime. At low <N>, the mean pair and triple counts are well below Poisson expectations, with important consequences for small scale behavior of 2- and 3-point correlation functions. The HOD depends strongly on galaxy age, with high mass halos populated mainly by old galaxies and low mass halos by young galaxies. The SPH simulation supports several simplifying assumptions about HOD bias: the most massive galaxy in a halo usually lies close to the center and moves near the halos mean velocity; satellite galaxies have the same radial profile and velocity dispersion as the dark matter; and the mean occupation at fixed halo mass is independent of the halos larger scale environment. By applying the SPH and SA HODs to a large volume N-body simulation, we show that both methods predict slight, observable departures from a power-law galaxy correlation function. The predicted HODs are closely tied to the underlying galaxy formation physics, they offer useful guidance to theoretical models of galaxy clustering, and they will be tested empirically by ongoing analyses of galaxy redshift surveys. (Shortened)
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