Since this washer was there, and there's a basement, Im going to go ahead and guess there are a set of double tubs there. Ideally what would happen is you would fill the washer with your wash water, placing the washer in front of the leftmost tub. Then you'd fill both tubs with your rinse water. Oftimes you'd put softener or bluing in the final rinse water. Lord willing, the pressure has been released on the rolls for storage, and on most Kenmores you re-engage it by lifting up on the end piece of the wringer, which will be ajar if the pressure is released. Some have a switch below the wringer power lever that you pull and release to re-engage the pressure.
You'd wash the clothes in the washer (there should be a switch for the motor, and switch or lever to start and stop the agitation). After washing, run them through the wringer into the first rinse water. On the left of the wringer there will be an on/off directional switch for the wringer, and a switch above or below it to release the head to position it where you want to wring. At this point, you could start another load washing in the washer. Then, you'd move the wringer to the center of the tubs, and run the clothes from the first to final rinse water. Finally, you move the wringer to the edge of the second tub, and wring from your final rinse water to your basket. By this time, you're just about ready to start the process again with the second load of clothes that have been washing erstwhile.
I believe most if not all of the Kenmore washers have electric drain pumps, the switch will be either on the front or the side. They usually have timers too that don't always work, but you can use the machine without it. If it does, you can set a time and the washer will stop at the end. At the end of the washday, you drain the tubs, then the washer, and you can use a hose to rinse and clean out the washtub with your drain pump open.
Now, unplug the washer and release the pressure on the rolls.
