To construct a Lineweaver-Burk plot, you start by conducting a series of enzymatic reactions at varying substrate concentrations. For each concentration, you measure the reaction rate. Using the Michaelis-Menten equation, the data points are then converted into their reciprocal forms. The y-axis represents 1/v (the inverse of the reaction rate), while the x-axis represents 1/[S] (the inverse of the substrate concentration).