A potentiometer is a variable resistor that is most commonly used as a volume control in consumer electronics. It usually has three connection pins and the amount of resistance can be controlled by turning a knob, dial or screw. For a 10k (10,000 ohms resistance) potentiometer, the amount of resistance can be adjusted from nearly zero ohms to around 10,000 ohms. A potentiometer is a very useful component because you can also vary the amount of voltage and current going through it by varying the amount of resistance.
Obtain the manufacturer's data sheet for your potentiometer and identify the three pins. One pin should be labelled "A" or "1" , one pin should be labelled "B" or "3" and one pin should be labelled "W", "2" or "wiper". There may even be markings for the pins on the potentiometer.
Measure the resistance of the potentiometer with a digital multimeter on the "ohms" setting. Set the meter to 20k because the actual value may measure slightly above 10k. Attach one meter lead (either one) to pin A and the other lead to pin W. Turn the potentiometer adjustment knob and you should see the resistance change according to the turning direction. Set the potentiometer to the midpoint, around 5,000 ohms.
Place the potentiometer on the breadboard and connect the negative wire of the five-volt power source (this will also be circuit ground) to pin B.
Connect the longer leg (pin) of the LED to pin W of the potentiometer and connect the shorter leg of the LED to the negative wire of the power source (or to pin B of the potentiometer). You may have to use extra wires to make connections.
Connect the positive wire of the power source to pin A of the potentiometer. Adjust the potentiometer knob and you should see the LED become bright or dim, depending upon the adjustment direction. When the LED is bright, potentiometer resistance is low (between pins A and W), more voltage is "used" or "dropped" and more current is fed to the LED. When it is dim, resistance is high, voltage is low and current is low.
The highest value of the potentiometer can measure above or below 10k. There is always a percentage of variance in the resistance, called tolerance. Common tolerance values for potentiometers are 5%, 10% and 20%. This means that, for 20% tolerance, the highest value of a 10k potentiometer can actually range from 8,000 to 12,000 ohms. In general, pin A and pin B can be interchanged. Just like a fixed resistor, most potentiometers are not polarised or directional. Pin W is the important pin. In a schematic, a resistor with an arrow pointing to the middle means that it is a potentiometer. The arrow is pin W.
Don't leave the LED on a bright setting. Too much current can damage it and it may become hot to the touch. If it starts glowing a different colour than normal, it is receiving too much current and power should be immediately disconnected.