LEDs are current-sensitive devices. Even a small increase in voltage above the 3.6V limit can cause the LED to draw too much current, leading to overheating and permanent failure.
How to Connect
Identify the Long Lead (Anode/Positive) of the LED.
Solder the resistor to either lead (it doesn't matter which side, but usually, it's added to the Positive side for consistency).
Connect to your power source.
Pro Tip for Robogears Customers: If the LED is too bright for your project, increase the resistor value (e.g., use a 1k $\Omega$ instead of 470 $\Omega$ on 12V) to dim the light and save battery power.