To test a potentiometer.
Measure the total resistance:
Connect one probe of your multimeter to each of the outer terminals of the potentiometer.
The multimeter should display a resistance value. This value should be equal to the total resistance of the potentiometer, which is usually printed on the body of the component.
Measure the wiper resistance:
Move the wiper to the center of the potentiometer.
Connect one probe of your multimeter to one outer terminal and the other probe to the wiper terminal.
The multimeter should display a resistance value. This value should be approximately half the total resistance of the potentiometer.
Rotate the potentiometer through its full range, looking for dead spots or other erratic changes. The resistance should change smoothly from maximum to minimum and back.
You can also check them with the power on by measuring the voltage. If I remember correctly, the voltage is only 5 volts DC.
I'm an old-school electronics technician, so I prefer an analog meter for this test and have a Simson 260 just for this sort of thing. However, you can do it with a cheap digital meter.