The dynamics of nucleation barrier crossing is examined using Becker-Doring kinetics, matrix methods, and stochastic model simulation. Fundamental connections between resistance to crossing and fluctuations in cluster size are derived using the Kubo-Nyquist relations. For analysis of nucleation kinetics, the matrix approach of Shugard and Reiss is supplemented with a novel extension based on recursion/projection operator methods. The combined approach yields nested sequences of upper and lower bounds to the relaxation rates of clusters coupled to a thermal bath. Fluctuations are studied using simulations based on a stochastic model of cluster evaporation/growth. Under typical conditions, it is found that relaxation from the top of the barrier is slow, due to multiple re-crossings, and the transmission coefficient for nucleation is small and extremely difficult to estimate from single-cluster simulations using standard Bennett-Chandler and Krainers models. A new approach based on relaxation on a "dual" potential surface is introduced. It is shown that the dual model provides an optimal weighted cluster sampling and reliable estimation of the transmission coefficient (to within a few percent). Collectively, these methods address the efficient determination of nucleation rates from computer simulations of individual cluster evaporation/growth events.