Potentiometers are variable voltage dividers with a shaft or slide control for setting the division ratio. They are manufactured in panel-mount as well as breadboard (printed-circuit board) mount versions. Any style of potentiometer will suffice for this experiment.
The two outside leads of the potentiometer act as a fixed resistor. As you turn the knob, a movable third lead called the wiper moves across the resistor, producing a variable resistance between the middle lead and either of the two sides. This results in a variable value that can be read at the middle lead. In this case between 0 and 1024. In the picture right below, the knob controls the wiper which is the thick black line turning clockwise and counterclockwise.
The potentiometer has 3 leads (the 3 small hoops sticking out on top of the pot), that we will be connecting to Power, Signal and Ground lines. The first thing you will need to do is connect the leads. For this you can either solder some wires to the 3 leads, or use alligator clips (in picture below) and attach one side to the pot lead, and another side to the wire.
If you salvage a potentiometer from an old radio or other audio device, you will likely be getting what is called an audio taper potentiometer. These potentiometers exhibit a logarithmic relationship between division ratio and shaft position. By contrast, a linear potentiometer exhibits a direct correlation between shaft position and voltage division ratio.
[ Fig-2: Potentiometer Construction]