Starting from the global parametrized post-Newtonian (PPN) reference system with two PPN parameters gamma and beta we consider a space-bounded subsystem of matter and construct a local reference system for that subsystem in which the influence of external masses reduces to tidal effects. Both the metric tensor of the local PPN reference system in the first post-Newtonian approximation as well as the coordinate transformations between the global PPN reference system and the local one are constructed in explicit form. The terms proportional to eta = 4 beta - gamma - 3 reflecting a violation of the equivalence principle are discussed in detail. We suggest an empirical definition of multipole moments which are intended to play the same role in PPN celestial mechanics as the Blanchet-Damour moments in general relativity. We also show that the tidal gravitational field as seen in the local PPN reference system can be expanded into powers of local coordinates similar to the tidal expansion in general relativity. Starting with the metric tensor in the local PPN reference system we derive translational equations of motion of a test particle (an Earth satellite) in that system. The translational and rotational equations of motion for center of mass and spin of each of N extended massive bodies possessing arbitrary multipole structure are derived. All equations of motion are presented also in the form of multipole expansions. Several interesting features of the equations are discussed. As an application of the general equations of motion a monopole-spin dipole model is considered and the known PPN equations of motion of mass monopoles with spins are rederived. For the first time, these equations are derived in a self-consistent manner which does not require any additional assumptions about the behavior of bodies such as secular stationarity.