How to add elements to an empty array in PHP?

Both array_push and the method you described will work.

$cart = array();
$cart[] = 13;
$cart[] = 14;
// etc

//Above is correct. but below one is for further understanding
$cart = array();
for($i=0;$i<=5;$i++){
    $cart[] = $i;  
}
echo "<pre>";
print_r($cart);
echo "</pre>";

Is the same as:

<?php
$cart = array();
array_push($cart, 13);
array_push($cart, 14);

// Or 
$cart = array();
array_push($cart, 13, 14);
?>