Limit current to something reasonable like 10..20mA (pretty much any led will tolerate 10mA and 10mA is big enough for power supplies to measure)
Set voltage to some low value like 1v
connect led in circuit.
Slowly increase voltage while monitoring current
When you get close to the forward voltage, led will start to conduct and current will rise.
Leds have a very narrow region where they behave like partially open, like there's something chocking current flow
For example (using bogus numbers) a white 100mA 3.2v led may be fully closed up to 2.8v and then between 2.8v and 2.9v it may be partially on, letting 1..10mA flow through...
and once you go over 2.9v it may be fully open letting hundreds of mA go through if you don't limit current.
But, you can't rely on these values as they're dependent on led temperature. it may be 2.8v..2.9v at 25..30c ambient but if you just turned off the led after an hour of running and led is 50-60c warm, that narrow region most likely drifted to something like 2.75v..2.85v
If you limit psu to 10..20mA and ramp voltage slowly you'll see the current jump from nothing to 10..20mA. It's also big enough value to see individual diodes if led is made with multiple diodes in series... ex a 6v led may be made with 2 leds in series inside package.
If psu won't let you limit current, you can make your own with a linear regulator
ex see the plain LM317 regulator:
http://www.ti.com/lit/ds/symlink/lm317.pdfSee page 12, section 8.3.3 ... how to limit current Iout = 1.2 / R1 ... so for example if you want to limit current to 20mA (0.02A) then 0.02 = 1.2/R1 so R1=1.2/0.02 = 60 ohm
This is not a
standard E12 or E24 value but 56 ohm or 62 ohm is and they're close enough, instead of 20mA you have maybe 18..22mA which is still good enough. If worried, you can recalculate for 15mA and then pick closest resistor standard value.
So you can feed 5v..12v to lm317 and you get on the output some voltage with a current limit.
Now you can use a second LM317 in standard adjustable configuration (see page 10, 8.2) ... with potentiometer you can adust output voltage from minimum 1.25v to input voltage minus ~ 1..1.5v
And note that the regulator itself will consume around 5mA so if you limit current to 20mA only with first regulator and 2nd regulator consumes ~5mA+ then led may only get 10..15mA