How do determine which resistor to use?

There is an LED calculator:

http://led.linear1.org/1led.wiz

Plus some of the links there explain the theory.

Given that Ohm's Law is: V = I * R

To calculate R you need: R = V / I

An LED will have around a 2V forward voltage drop (see the datasheet for exact figures) so you need to drop 3V (5V - 2V) if you are plugging into an Arduino output pin.

Generally you might want 20 mA (0.020 amps) to light the LED. So substituting you get:

R = (5 - 2) / 0.020 = 150 ohms