basic LED functions

Well, lots of things not quite right there.
First, when posting code, please use the #(Code) button in the editor.

ledPins has only three entries, but you've got odd constructs like:
" pinMode(ledPins [2, 3, 4], OUTPUT); " (I'm surprised this compiled!)
and
"digitalWrite(ledPins [3], LOW);" (The largest subscript of "ledPins" is 2)
Try:

int ledPins[] = {
2, 3, 4 }; // An array of pin numbers to which LED's are attached

// The setup() method runs once, when the sketch starts

void setup()   {                
  // initialize the digital pins as an output:
  for (int i = 0; i < sizeof (ledPins) / sizeof (ledPins [0]); ++i)
    pinMode(ledPins [i], OUTPUT);     
}

// the loop() method runs over and over again,
// as long as the Arduino has power

void loop()                     
{
  digitalWrite(ledPins [0], HIGH);   // set the LED on
  delay(300);                        // wait for a second
  digitalWrite(ledPins [0], LOW);    // set the LED off
  delay(300);                        // wait for a second
  digitalWrite(ledPins [1], HIGH);
  delay(600);
  digitalWrite(ledPins [1], LOW);
  delay(600);
  digitalWrite(ledPins [2], HIGH);   
  delay(1000);                 
  digitalWrite(ledPins [2], LOW);    
  delay(1000); 
}