Brand new to Arduino, and can't even make an LED blink So I'm going through Getting Started With Arduino. I skipped to making a LED blink when you press a button.

First I wrote the code, then I copied it directly from the .pdf I have, neither has worked.

The code is here:

// Example 02: Turn on LED while the button is pressed
const int LED = 13;   // the pin for the LED
const int BUTTON = 7; // the input pin where the
                      // pushbutton is connected
int val = 0;          // val will be used to store the state
                      // of the input pin
void setup() {
  pinMode(LED, OUTPUT);   // tell Arduino LED is an output
  pinMode(BUTTON, INPUT); // and BUTTON is an input
}
void loop(){
  val = digitalRead(BUTTON); // read input value and store it
  // check whether the input is HIGH (button pressed)
  if (val == HIGH) {
    digitalWrite(LED, HIGH); // turn LED ON
  } else {
    digitalWrite(LED, LOW);
  }
}
Other than what what Nick Gammon said that you need the resistor from the board to led, as that will cause your microcontroller pins to get damaged.

The other possible problem is the two breadboards you have put together, the power rails have not been bridged between the two boards. This means that the switch is not providing any logical state to the microcontroller.

Also the only reason why the led is show in the book as a separate thing is that it is meant as an educational exercise to make you build something, the L led will do the same thing.