  We study the properties of potential new Z' gauge bosons produced through the
Drell-Yan mechanism at the LHC. Our analysis is performed using a fully
differential next-to-leading order QCD calculation with spin correlations,
interference effects, and experimental acceptances included. We examine the
distinguishability of different models and the feasibility of extracting
general coupling information with statistical, residual scale, and current
parton distribution function error estimates included. We extend a previous
parametrization of Z' couplings to include parity-violating coupling
combinations, and introduce a convenient technique for simulating new gauge
bosons on-peak using the concept of basis models. We illustrate our procedure
using several example Z' models. We find that one can extract reliably four
combinations of generation-independent quark and lepton couplings in our
analysis. For a Z' mass of 1.5 TeV, one can determine coupling information very
well assuming 100 fb^{-1} of integrated luminosity, and a precise measurement
becomes possible with 1 ab^{-1} at the SLHC. For a 3 TeV mass, a reasonable
determination requires the SLHC.
