Suppose you are looking at a chemical reaction and only the chemical reaction is given. What experiments, mathematical equations, theories, and graphs would you have to compile to describe the rates and order of the reaction?

I am aware that the experiments should include an excess/constant concentration of one reactant and then varying the concentration of the other reactant. Then the initial rate should be recorded. The experiment is then repeated with the other reactant.

Is there anything other than gathering the initial rate data and plotting the ln of each side of the initial rate equation in a graph for determining the constant? How would this help determine the order?