You can't really predict the rate-limiting step theoretically, short of doing an explicit quantum-chemical calculation. In fact, it's difficult to predict any of the steps. Most of the time you're doing educated guesses based on chemical intuition and similar known mechanisms. Determining the reaction order is relatively simple to do experimentally (plot concentrations versus time basically), and also the transition state energy (same experiment, but vary the temperature so you can determine dS). Depending on your interest, this is often good enough - as one professor told me as an undergrad - it doesn't really matter if you have two or fifty intermediates, if they're not rate-limiting.
On the other hand, if your main interest is in catalysis, and the details of how the reaction occurs, it's tricky. The only way to "directly" observe the reaction is to use ultrafast laser spectroscopy, which is difficult and still a fairly rare procedure. There's a whole host of experimental techniques to try to glean information though, looking for bireactions; reacting with analogues, using isotope labeling of certain atoms to see where they end up, using various reactants and tricks to 'trap' the reaction at some intermediate that you can characterize, looking for kinetic isotope effects (e.g. a deuterium bond will break more slowly than a hydrogen bond since it's heavier and slower), and so on.
Then there's pure theory (what I do), which is to test the plausible mechanisms and use quantum chemical methods to calculate the theoretical transition-state energies for the various methods. QC methods aren't yet accurate enough (in most cases) to correctly predict kinetics, but they're at least accurate enough to give an idea of which mechanisms are more likely and which ones are certainly impossible.