They are created with the corresponding constructors and factory functions:
val arrayOfZeros = IntArray(size) //equivalent in Java: new int[size]
val numbersFromOne = IntArray(size) { it + 1 }
val myInts = intArrayOf(1, 1, 2, 3, 5, 8, 13, 21)
T can still be one of types primitive in Java (Int, Boolean,...), but the values inside will be boxed equivalently to Java's Integer, Double and so on.
val nulls = arrayOfNulls<String>(size) //equivalent in Java: new String[size]
val strings = Array(size) { "n = $it" }
val myStrings = arrayOf("foo", "bar", "baz")
val boxedInts = arrayOfNulls<Int>(size) //equivalent in Java: new Integer[size]
val boxedZeros = Array(size) { 0 }