The adjustment range is approximately 0–30 mA, which is suitable for testing all normal LEDs. If you wish, you can connect a multimeter across the LED to measure the voltage on the LED. For the power source, a good option is to use a small laboratory power supply with the output voltage set to 5 V. It is convenient to fit the potentiometer with a scale so you can see directly how much current is fowing through the LED. In order to calibrate the scale, you can temporarily connect an ammeter in place of the LED.
Circuit diagram:

LED Tester Circuit Diagram