Park the mower in a location with a flat surface with room to work, such as inside a garage. Set the parking brake. Turn off the ignition and remove the key.
Open the engine hood, or remove it entirely if possible on your model.
Grasp the rubber boot covering the spark plug that sticks out of the side of the engine. Pull the boot straight up and off to remove it from the plug.
Place a bucket on the ground near the engine. Loosen the hose clamp holding the gas line in place with a pair of pliers or a screwdriver as needed. Pull the fuel line off the carburetor and place it into the bucket to catch the gas.
Loosen the screw or nut holding the throttle linkage in place underneath the carburetor.
Loosen the bolt securing the terminal for the red wire on the battery. Pull the red terminal off of the battery.
Use a torque wrench or socket wrench to remove the bolts securing the engine to the riding chassis.
Put on a pair of heavy work gloves to protect your hands. Slowly tilt the Kohler engine forward. As you do so, grasp the drive belt with a gloved hand or pair of pliers and pull it so it slides off the pulley adjacent to the crankshaft. Once the belt is free, pull the engine off the riding mower chassis.
Align the new engine in the block with the crankshaft pulley at the rear. Grasp the engine belt and slip it over the engine crankshaft pulley. Check that the belt is fully within the pulley channels and make adjustments as needed.
Secure the engine in place on the chassis with the engine mounting bolts.
Slip the fuel line over the carburetor nipple and secure it with the clamp. Reconnect the throttle linkage.
Slip the spark plug boot back over the plug.
Reconnect the red wire to the battery and tighten the terminal in place.