Realistically, almost no reactions happen in a single step.
This is mostly a matter of statistics; the odds of more than two molecules colliding at once are small.
Therefore, most reactions have a series of steps, and the energy diagram looks less like the first picture on the right, and more like the others--lots of bumps.
The dips labeled 'I' are intermediates--things made in the reaction then immediately used up. They are typically short-lived and very reactive; the formulas often look 'wrong'.
The series of steps to get from reactants to products is the mechanism. You can never completely prove a mechanism, but to even be possibly valid, it must meet two criteria:
1. It must add up to the overall reaction.
2. It must match experimental data (typically the rate law, but sometimes more is known).
O3 + 2NO2 → N2O5 + O2
One possible mechanism for this reaction is:
Step 1: O3 + NO2 → NO3 + O2
Step 2: NO3 + NO2 → N2O5
The nitrogen trioxide is an intermediate.
If a catalyst were present, it would be in the reactants first, then come out as a product in a later step.
In each case above, the arrow shows the overall activation energy of the reaction--the highest hill to get over.
The step with the highest energy barrier is the rate-limiting step aka the rate-determining step. The rate of this step will be the one that is responsible for the experimental rate law for the reaction.
You can determine the order from the coefficients in a mechanism.
In the example mechanism to the right:
* If the first step is the slow step, then:
Rate = k[O3][NO2]
*If the second step is slow, then:
Rate = k[NO3][NO2]
But nitrogen trioxide is an intermediate, which we don't want in our rate law, since we can't measure or control it. Since it came from Step 1, though, we can substitute in for it:
Rate = k[O3][NO2][NO2] = k[O3][NO2]2