Question: Can you explain how the order of a reaction is related to its mechanism?

Answer: Typically, the order of the reaction indicates the number of molecules that need to come together to form the transition state.  For example, in a second order reaction, the transition state will have two molecules colliding with one another.  Keep in mind that this only gives you information about the rate-determining-step, as other steps aren't involved in determining the rate of reaction.

This also explains why there are very few third and fourth order reactions.  It's pretty rare that three molecules can all come together at the same time and in the right geometry to undergo a chemical reaction.