Resistor values for a series circuit

[roam]

Suppose we have a bulb or a forward-biased LED (or any other component) which needs no more than say 3 V across it to operate. And we want to connect it in series with a voltage source of say 12 V, and a resistor. So without this resistor, the LED would quickly burn out and be destroyed.

I've edited a diagram to illustrate the situation:

[PLAIN]http://img225.imageshack.us/img225/6515/circt2.jpg

How can we calculate the value of this resistor in series with the LED and the battery, that limits the current flow through the LED to a safe value, and reduce the 12 V to 3 V? I know that there many websites and softwares that can calculate the value of the resistor, but I just want to know how engineers would do the calculation without using them. Is there a quick method or a formula?

And what if there are two (or more) LEDs instead of just one?

I couldn't find any methods for this in my physics textbook so any guidance is greatly appreciated.

 

[mdjensen22]

For an LED, take the forward voltage drop rating (Vf) from the datasheet.
Add all of those forward voltage drops together for multiple LEDs. If you don't have a datasheet, you can make assumptions (~2V for red, etc.)
Subtract that number from your source voltage. This give the voltage drop across the resistor.

Then it becomes a simple Ohm's law calculation (V=IR) - if you know the current you want to use, then you need to solve for the resistance - Take the voltage across the resistor and divide by the desired current to get the resistor value.