So, I was going through the spec sheet of super bright 5mm orange LED, and it was listed that the forward voltage is between 1.8V and 2.5V. Below that there was a property listed as 'typical voltage' and had a value of 3.2V. I'm confused as to what value of resistance I must use.
The important thing to realize is that CURRENT is what MATTERS to an LED. The voltage is given as a range because the voltage varies, depending on manufacturing tolerances, temperature, etc.
If you design well for LEDs, you feed them with a current source, and the voltage simply needs to be adequate for the number of LEDs you have in series on each current source. In figuring the voltage compliance your current source should have, look at the highest voltage quoted.
If you use resistors for current-limiting LEDs, use either the LOWEST value of forward voltage provided, or a bit less than that (safety margin) when choosing a resistor to set the current. This is sub-optimal .vs. a current source, as it will generally be providing less than the maximum safe current in order not to provide more than the maximum safe current under conditions (or for parts) where the forward voltage is particularly low.
Quick solution. If you want to know the forward voltage hook your LED to a power supply turned down to 0 volts and slowly crank up the voltage.
You LED will turn on once forward voltage is reached.
However, you might blow an LED up doing this so proceed with caution.
To help answer your question. Use forward current to decide on what resistor to use and take the worst case forward voltage.
If you have doubts on the stated specs, you can make a simple Constant Current regulator to test an LED out with a common adjustable LDO.
R1 can be a fixed resistor, or more conveniently, a variable resistor or trimpot. For 20 mA, that's 62.5 Ω. (R = V/I, in this case VRef / IOut).
Simply measure the voltage across the Load/LED and you know how much it's Forward Voltage Drop at 20mA is.