I have a Kenmore series 90 which wouldn't spin or agitate. Here is my experience:
I needed a few old towels, a couple of buckets, a pair of plyers, a flathead screw driver, and a hammer.
I bought a coupler for $16.26 at an appliance parts store. I unhooked all three hoses from the back, and water poured out! First, TURN OFF THE WATER!! Then put some towels down under where the hoses connect to the washer, so that they will catch the water which comes out. Have a bucket handy to put the hoses in, after you unhook them from the machine, so that they can drip into the bucket. You will also want a towel handy to wipe your feet on, when you walk back into the house.
If a towel gets soaked with water, it is handy to have a second bucket to put the wet towel in.
I also got a stopper to put over the drain connection, after I unhooked the drain line. Basically, I found a rubber baton end, and it fit tightly over the connection. If you don't do that, dirty water will pour out of the drain connection when you turn the washer on its back.
There were two metal straps holding the pump on the bottom of the motor. I used a flat-blade screw driver to pop them loose, then I put them on the side. I unhooked the drain line from the outlet side of the pump, and hooked it behind the frame of the washer, so that the open end stayed up! (So it wouldn't pour out its dirty water!) I loosened the clamp holding the inlet hose , and then turned the pump clockwise (?), so that the pump was away from the motor, and also so that the outlet connection pointed up! (again, so nothing would drain out of it).
I then removed the two straps holding the pump on, and the pump easily came off of its bracket. (The motor is really heavy compared to the pump, and so you will think it is still connected, but it probably isn't; its weight is holding it in place.)
I then discovered that the coupler was broken into multiple pieces. One piece was still attached to the motor shaft; one piece was still attached to the shaft on the washing machine; and the rubber piece which connects the two pieces was off by itself. I used a flat head screw driver to pry the two pieces off of the two shafts, then I removed all debris.
I then installed the new coupler. I needed to first line up the coupler's hole with the washing machine shaft, and then lightly tap it down with a hammer. I then rotated the motor's shaft till it lined up with the coupler's other hole, and I then pressed the motor's shaft down into the coupler's as far as it would go. But I hardly made any progress by hand, so I had to lightly tap on the other end of the motor's shaft with a hammer, till the motor's shaft was all the way into the coupler's hole. I then snapped the two straps back onto the motor.
I then realigned the pump with the top of the motor and reconnected the drain line to it. I then rotated the motor's shaft to line up with the hole on the pump, and I pressed the pump down onto the shaft by hand. (I had to rotate the shaft some more with plyers as I was remounting the pump.) I got the pump remounted by hand (no need for a hammer here), and I then snapped the two straps back into place on the pump.
I haven't yet been able to test the repair, because my hot water connection is leaking. But I'll replace the hot/cold entry connections tomorrow.
As far as the vibrations spoken of by Victor D, my guess is that he didn't have the coupler mounted completely onto one or both shafts. Tap it lightly with a hammer till it's all the way down.
Jim - New Orleans, January 2011