Create a standard rate equation of the form, Rate = [A] [B] k, where [A] and [B] are the molar concentrations of species A and B respectively (more may be used as needed), and k is the proportionality constant of the reaction. It is important to note that the exponents to which each molarity is raised can not be determined analytically. These values, along with k, must be determined experimentally in the lab or ascertained from a reference of an identical reaction.
Once you have determined the orders of all the species in the reaction, raise each species to its individual order in the equation. This is to say, if [A] is of the second order, then raise it to the second power, [A]^2. Repeat this for all species in the reaction.
Total the sum of all individual orders of reaction for all species within the reaction. This value is the overall order of the reaction. For example, the reaction represented by "Rate = [A] [B]^2 k" would be a reaction of third order. The value of 1 is assumed for any species which is not raised to a power, as is the case with [A] in this example.