The experimental determination of the properties of the newly discovered boson at the Large Hadron Collider is currently the most crucial task in high-energy physics. We show how information about the spin, parity, and, more generally, the tensor structure of the boson couplings can be obtained by studying angular and mass distributions of events in which the resonance decays to pairs of gauge bosons, ZZ, WW, and gamma gamma . A complete Monte Carlo simulation of the process pp arrow right X arrow right VV arrow right 4functionof is performed and verified by comparing it to an analytic calculation of the decay amplitudes X arrow right VV arrow right 4functionof. Our studies account for all spin correlations and include general couplings of a spin J = 0, 1, 2 resonance to Standard Model particles. We also discuss how to use angular and mass distributions of the resonance decay products for optimal background rejection. It is shown that by the end of the 8 TeV run of the LHC, it might be possible to separate extreme hypotheses of the spin and parity of the new boson with a confidence level of 99% or better for a wide range of models. We briefly discuss the feasibility of testing scenarios where the resonance is not a parity eigenstate.