First of all, I would like to say thanks to Kid Clock for providing the circuit, I would have never thought to do this.

After building this for myself, I found that I needed to understand how this worked and how the values were selected.

I will describe what I found in case this would benefit someone else as well.

From a similar discussion on the topic

http://cr4.globalspec.com/thread/13464/Capacitors-as-AC-Voltage-Drop-ComponentsI found the keyword here is capacitive reactance, basically (Xc) = 1/(2 * pi * f * C) where Xc is the capacitive reactance measured in ohms, f is the frequency (in our case 60) and C is the capacitance.

For our purpose, we want a reactance value that yields approximately 20 mA (the actual value of this circuit is about 21 mA so I will use that).

Using V = I*R we get R = 120/.021 which is about 5714 ohms. Putting this into the above formula we get 5714 = 1/(2*3.14*60*C) simplified as

C = 1/(377*5714) = ~.46 ?F which yields our capacitor selection.

Our resistor selection is based on the mentioned inrush current. To calculate this using the provided resistor value, we are estimating that the peak value is around 150VAC (actual is more like 170 but this works fine). Using these values, we get I = V/R = 150/1000 which is 150 mA, a generally safe value for most standard LEDs.

Edit: Not sure this bit on power is quite right, but this is why I'm not an electrical engineer

For determining the safest wattage of the resistor we can use the equation for power P = (I^2)*R. It appears that the above circuit is rated for the wattage provided after the initial inrush which seems to make sense as the period of inrush is momentary. Using our average current and calculated resistance we get P = (.02^2) *1000 = 0.4 W

Doubling the wattage as is a good practice yields using at least a one watt resistor. The resistor linked above is 3W making this look to be safe.

A good step by step of this can also be found here:

http://www.instructables.com/id/Using-AC-with-LEDs-Part-2-and-make-this-handy-/#step1