Empty the washer if there is still a load of clothes in it.
Slide the washing machine carefully out from the wall and then unplug it. Also, make sure the water connections are shut off and then removed from the back of the washer.
Remove the two top console screws with a Phillips screwdriver and then pop the console up and backwards. Also, disconnect the door switch plug.
Use the screwdriver to remove the screws or clamps, depending on the model of your Kenmore, from the back panel. Once these are loosened or removed, go ahead and pull the front cover forward and slide it out so that you can access the rest of the washer.
Remove the agitator cap and then use a socket set to remove the agitator bolt from the top. Lift the agitator out of the washer tub.
Remove the Kenmore motor's plastic wiring harness and pull the pump loose from the motor by removing their retaining clips with a pair of pliers. Removing the pump hoses is not necessary to access the motor and transmission.
Use the socket set to remove the bolts holding the motor in place. Slide the motor loose and set it aside.
Put the washer on its back and then use the socket set to remove the transmission gear case. Pull the old transmission. Hold the new one in place, insert the retaining bolts and then tighten them down with the socket set.
Install the motor and tighten it down with its bolts. Plug the motor's plastic wiring harness back in. Hold the pump back in place on the motor and replace the retaining clips with the pliers. Set the washer back up into the upright position.
Lower the agitator back onto the agitator shaft, replace the retaining bolt with the socket set and then put the cap back on.
Slide the front and side panel back onto the chassis of the washing machine and replace the clips or screws on the back panel to hold it in place.
Connect the door switch plug, lower the console and replace the screws. Reconnect the hoses to the back of the machine and plug it back in,