The photoproduction of vector mesons (rho, omega, phi) is of renewed interest because intense high energy beams of polarized electrons and photons are under development. These beams and also polarized targets make it possible to explore the dynamics of basic baryon structure. As a step toward that goal, an analysis of all possible polarization observables for the case of vector meson photoproduction from a nucleon target is presented. The question of which observables are needed to determine completely the basic photoproduction amplitudes and the relationships between spin observables are addressed. Such theorems are most readily demonstrated by representing all observables as bilinear products of helicity amplitudes and using known properties of Dirac gamma and spin-1 matrices. The general angular dependence of spin observables, especially near thresholds and resonances, is examined for the vector meson case. The criteria for a complete set of observables and the relationships between observables are then presented.