Calculating LED resistors is very straight forward if you help yourself out and use the known variables of the LED. This is assuming you have voltage supply -> resistor -> LED(s) in series with no current branches between the LED and the series resistor (you can have currents branch from the voltage supply into other pairs like in your circuit, this won't change the calculation).The three voltages you must use:
Supply Voltage - known - you pick this, but realize it must be high enough to drop across a resistor and LED.
LED Voltage - known - You kind of pick this too, its the values you have in your drawing, and its given in the datasheet. This is the desired operating voltage for the color LED you chose. It may be different in the end from what you designed it for because you might choose a lower current, and because of the I-V relationship of its diode nature, but you don't worry about that.
Resistor Voltage - unknown - This is the voltage you don't know initially, and so you must calculate it given the other 2 knowns.Using KVL:
Resistor Voltage = Supply Voltage - LED Voltage (if you have more than 1 LED in series, sum their voltages together)
Now, you know all 3 voltages, and the only thing left to do is calculate your resistance value. This is determined by choosing how much current you want to put through the LED. You have the maximum current ratings for all the LEDs already found in the datasheet, so you can use those values, but they'll be very bright and on the edge of recommended operating current.
You might want to lower the brightness or power consumption, and so choosing 10-15mA should be more than bright enough in most uses (you can always reduce your resistor values later to get more current and make it brighter). Your LED datasheet probably has an I vs V curve which is common to other diodes too, and so your minimum current to get the desired LED voltage drop is found there, but you don't need worry about this detail if it doesn't make sense to you; if you pick anything more than 5 mA, you're probably safe.
So, let's say we want 10mA through the LED. Applying KCL says that the same current in the LED(s) must pass through the resistor. Now we just use Ohm's law to calculate the resistor value.
R = V/I = Resistor Voltage/10mASo that's how you can calculate the resistance value. The only thing left is to make sure that your physical resistor package is appropriate. If you choose a bigger voltage supply value, then you are going to have a larger voltage drop across your resistor for a given LED drop, and so the resistor's power dissipation will increase for a given LED current. Calculate the power the resistor dissipates using R*I^2 or equivalently, Resistor Voltage * I, and make sure the physical resistor package is rated for that much power.
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