We present a method for developing potential-energy surfaces for abstraction reactions with four or more atoms which combines spline fits to high quality ab initio results for the three degrees of freedom that are most active in the reaction (two stretches and a bend) with simple empirical functions (Morse stretches, cosine bends, and torsions) for the spectator variables. The geometry and force constants associated with the spectator modes are allowed to vary along the reaction path so as to match stationary point properties from the ab initio calculations. In an application of this approach to the H + H2O reaction, we are able to generate a global surface for the H3O system that accurately matches ab initio properties, and is globally smooth and free of artifacts. Quasiclassical trajectory (QCT) calculations are used with this surface to study the H + H2O reaction dynamics for both the ground and local mode excited states. The resulting ground-state angular distributions, product state vibrational and rotational distributions, and rotational alignment factors are in excellent agreement with all known experiments. This represents an improvement over the results obtained using previous surfaces, but like the past surfaces, the calculated integral cross sections are below experiment by at least a factor of 2. For studies of the H + H2O reaction involving local mode excited states of water, the new surface is consistent with ab initio threshold behavior, with the (04)(-) local mode state having zero activation energy. However the reactive rate coefficients are substantially smaller than the observed total reactive plus inelastic rate coefficient. This indicates that recent experiments due to Barnes, Sharkey, Sims, and Smith are dominated by energy transfer rather than reaction.