In order to determine the overall reaction order, we need to look at the rate law. Rate law has a general formula Rate = k[A]^m [B]^n where A and B are reactants. Rate law can also look like this Rate = k[A]^m if there is only one reactant in the equation or it can have more reactants depending on the equation given.
In order to determine the overall reaction order all we need to do is simply add the exponents of the reactants listed in the rate law. Thus, Rate = k[A]^1[B]^2, is third order (1+2=3), and Rate = k[A] is first order since there is only one reactant with the exponent equal to 1.