If you have a power supply with adjustable current limit (like this one), then it becomes very easy.
- Set the output voltage to around 5V.
- Dial and dial the current limit all the way down.
- Connect the diode directly to V+ and COMthe power supply, with no resistor. Don't worry! You've already limited the current!
- Dial up the current until it reaches your target (say, 20mA).
The power supply is limiting the current through the LED to the dialed-in limit. The voltage display will show you what voltage is required to push that much current. That's your forward voltage!