How do I measure the voltage drop between LEDs? An ohms meter?
You can measure voltage by using the voltage setting on your multimeter. I'm assuming you have a multimeter. If you don't have one, get one as you will surely need one eventually.
For your purpose, it is not the voltage drop
BETWEEN LEDs that you should be concerned with. In between the LEDs is just wire which will have a negligible voltage drop for your circuit. What you need to determine is the voltage drop
ACROSS the current limiting resistor (shown as 180 in the attached schematic). I know there are 4 of them. Just pic one. The results will be nearly the same for all.
Refer to the attached schematic. You need to measure the voltage between points A and B. You do this by placing the multimeter in parallel with the resistor. Once you select the voltage setting on your multimeter place the positive (red) lead on point A and the negative (black) lead on point B. Now power up the circuit. The voltage you measure will change depending on whether the green or yellow LED is lit. Record both voltages you see and calculate the difference. The difference is what you must account for with your extra resistor.
You're not done yet. You still need to measure the current through the resistor. You'll have to measure the current differently than you did the voltage. First select the current measurement on your multimeter. It will most likely be marked "mA" or "A". You'll also have to change where the positive (red) lead plugs into your multimeter as most multimeters have one jack for voltage measurement and another for current.
Once your multimeter is reconfigured, hook it up like it shows in the schematic. You'll need to measure the current by placing the multimeter in series with the resistor. You should still do this with the resistor you measured the voltage at, I just showed it with a different resistor in the schematic for clarity.
Like with the voltage measurement, the current measurement will change depending on whether the green LED or yellow LED is lit. Record the current that you measure when the green LED is lit.
Once you measure the current, calculate the necessary resistor value using Ohms law.
V = IR or R = V/I since you want to find R. Pay attention to the units and remember that 1 mA = .001 A. The units you should use when you calculate the reststance is Volts and Amps.
I read something each resistor automatically uses up 2Vs or something?(read it on the LED page on the putting LEDs in series part
Light Emitting Diodes (LEDs) I dunno if I understood it wrong?)
There is no standard voltage drop across a resistor. I think you misunderstood what was written on that site. The voltage drop across the resistor totally depends on the supply voltage, the number of LEDs, and the color of the LEDs. Each LED has a set voltage drop depending on its color and how much current it's conducting. That is most likely what they are talking about.
Could I possibly keep adding more 47k Resistors in the point till I get the desired light change speed?
Yes, 2 47KΩ resistors in series is equivalent to one 94KΩ resistor. 3 would be equivalent to a 137 KΩ and so on.