Diode and resistor series
The so-called forward voltage can be found in the datasheet. If you don't have a datasheet, than find a few different ones, and check the average for the color of your LEDs (most LEDs with the same color have a (small) range of forward voltage.

Once you know that, use the following formula:

V - Vfw = I * R  where

V : Voltage
fw: Forward voltage of the LED
I : Current
R : Resistance


Assuming you have a LED with forward voltage 1.7 V, than your formula will result in

9 - 1.7 = I * 100 &lt;=&gt; I = (9 - 1.7) / 100 = 0.073 A = 73 mA


Btw, this is probably way too much, since most LEDs (3mm) have a limit of around 20 mA or 40 mA. Assuming you want 20 mA, you have to increase your resistor value (using the same formula above, I will leave this up to you).

Update

I now see the exact type of your LED, using a datasheet of it (e.g. LTL-307EE Datasheet, it shows a forward voltage of typically 2.0 V.

This means in your case the current will be

(9 - 2) / 100 = 70 mA


Although it can stand short peaks of 120 mA (see also datasheet), the continuous forward current is 30 mA. So if you want to have it continously lit at max current, than the resistor value should be:

(9 - 2) / R = 0.03 &lt;=&gt; R = (9 - 2) / 0.03 = 233 ohm


The next common higher resistor value is 270 ohm which results in a current of

(9 - 2) / 270 = 26 mA


Update 2

When looking at figure 2, at 30 mA, the forward voltage is 2.1 V, so the current is actually

(9 - 2.1) / 270 = 25.6 mA.