Measure the width and depth of the base of your evaporative cooler. Write down the measurements.
Cut two boards that equal the length of the cooler's width with your miter saw. Subtract 3 inches from the depth measurement and cut two boards at this length.
Check the manual for your cooler to see if the bottom of your cooler needs air flow for convection or for cooling. If it has these requirements then drill 1-inch holes through the four boards cut in the previous step. The holes should be all the way down the 1 3/4-inch face of the board, spaced 1-inch apart. The two outside holes should be 1-inch away from the ends of the boards.
Set the two boards that were cut for the width on edge, parallel and spaced the measurement of the depth minus 3-inches. Place the last two boards perpendicularly between them on edge so their sides are flush with the ends of the first pair of boards used in this step. Screw through the boards cut for the width of the cooler and into the ends of the other boards. Use eight screws for this step.
Set your 2 x 4 stand on a level area where you want to mount your cooler. Set your cooler on the stand and proceed with further installation according to your manual.