Restoring an old washing machine to working order involves cleaning the agitator, putting in new components such as belts and gear boxes, and cleaning the pump out. Sometimes older washing machines also need to have their motors replaced.
Debris and even socks can gather beneath the agitator in a washing machine of any age. Pull the cap off the agitator, slide the agitator up and out, and remove anything that has come to rest beneath the agitator to complete this part of the process.
Older washing machines use a belt to drive the motor. If the belt has snapped or looks ready to snap, it's time to put a new one in. Unplug the machine, take the back panel off, loosen the motor enough to take the belt out, and replace it with a reasonable facsimile from an appliance part store. To test whether the new belt is tight enough, push down on it between the pulleys. If it moves more than 1/2-inch, it needs some more tightening.
Finding a new motor can be tricky with older machines. Contact an appliance repair supply to make sure that it has a compatible motor before taking out the old motor. Unplug the washing machine from the wall when accessing the motor. Garbage tends to gather in the pump. In some older machines, the pump is a clear plastic cylinder; it sits behind the wires running to the motor. Take the pump apart to get rid of the debris and clean it out.