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);
}