The first thing you'll want to do with your Arduino Board will be to get it set in your breadboard and then add in a couple of wires so we have power hooked up to the rails down both sides of the board. Once this is done you should leave it together no matter what else you're doing.
The process is pretty straight forward. With some breadboards (like the ones we use in class) you won't need those little bits of wire on the side rails as the connection runs the length of the board.
LEDs have two legs, on most LEDs the shorter one is the negative lead. It is also important to note that LEDs will burn out if you put too much voltage through them. So you will almost always need to include a resistor. The exact size will vary with the specific LED and the voltage we're using. When in doubt 1k ohm is a good default. For our LEDs and Arduino 220 ohms works just fine. Now attach your resistor and LED to your Arduino, being sure that the short (negative) lead is attached to our negative power rail (or ground).