You might want to check this out:
Its not a real circuit simulator, but its close enough for educational purposes.
You can drag in various components like LEDs and power sources and it will help you visualize how the current is flowing
Playing around with this might give you a better idea of how the LED circuit is actually working.
There is a Java version of the sim that might run a little bit better then the in-browser one, link at the bottom....
I've been wanting to make my own version of this type of application, but haven't gotten around to it.
The Falsted simulator is unique from most simulators that I have seen in that its designed to be really easy to use intuitive.
Also, simulation is no substitute for playing around on a breadboard with some components :)