You want the splice function on the native array object.

arr.splice(index, 0, item); will insert item into arr at the specified index (deleting 0 items first, that is, it's just an insert).

In this example we will create an array and add an element to it into index 2:

var arr = [];
arr[0] = "Jani";
arr[1] = "Hege";
arr[2] = "Stale";
arr[3] = "Kai Jim";
arr[4] = "Borge";

console.log(arr.join()); // Jani,Hege,Stale,Kai Jim,Borge
arr.splice(2, 0, "Lene");
console.log(arr.join()); // Jani,Hege,Lene,Stale,Kai Jim,Borge

UPDATE (24 May 2024)

You can now use the toSpliced method which behaves just like splice, however it returns a new array without mutating the existing one.

You could update the previous example like so:

const updated = arr.toSpliced(2, 0, "Lene");

Use unshift. It's like push, except it adds elements to the beginning of the array instead of the end.

• unshift/push - add an element to the beginning/end of an array
• shift/pop - remove and return the first/last element of an array

A simple diagram...

unshift -> [array] <- push
shift   <- [array] -> pop

and chart:

Check out the MDN Array documentation. Virtually every language that has the ability to push/pop elements from an array will also have the ability to unshift/shift (sometimes called push_front/pop_front) elements, you should never have to implement these yourself.

As pointed out in the comments, if you want to avoid mutating your original array, you can use concat, which concatenates two or more arrays together. You can use this to functionally push a single element onto the front or back of an existing array; to do so, you need to turn the new element into a single element array:

const array = [3, 2, 1]

const newFirstElement = 4

const newArray = [newFirstElement].concat(array) // [ 4, 3, 2, 1 ]

console.log(newArray);

concat can also append items. The arguments to concat can be of any type; they are implicitly wrapped in a single-element array, if they are not already an array:

const array = [3, 2, 1]

const newLastElement = 0

// Both of these lines are equivalent:
const newArray1 = array.concat(newLastElement) // [ 3, 2, 1, 0 ]
const newArray2 = array.concat([newLastElement]) // [ 3, 2, 1, 0 ]

console.log(newArray1);
console.log(newArray2);

Use Array#unshift method.

var array1 = ["fruit", "vegetables"],
  array2 = [
    ["apple", "banana"],
    ["tomato"]
  ];

var array3 = array2.map(function(v, i) { // iterate over the array to generate the new array
  var arr = v.slice(); // copy the array
  arr.unshift(array1[i]) // insert element at beginning 
  return arr; /// return generated array
});

console.log(array3)

UPDATE : If you don't want to create a new array then you can avoid the copying part.

var array1 = ["fruit", "vegetables"],
  array2 = [
    ["apple", "banana"],
    ["tomato"]
  ];

array2.forEach(function(v, i) { // iterate over the array 
  v.unshift(array1[i]) // insert element at beginning 
});

console.log(array2)

With ES6 arrow function :

var array1 = ["fruit", "vegetables"],
  array2 = [
    ["apple", "banana"],
    ["tomato"]
  ];

array2.forEach((v, i) => v.unshift(array1[i]));

console.log(array2)

Multi purpose for ARRAY and ARRAY OF OBJECT reusable approach

let arr = [0,1,2];
let obj = [{ name: "abc"},{ name: "xyz"},{ name: "ijk"} ];

const addArrayItemAtIndex = ( array, index, newItem ) => {
    return [...array.slice(0, index), newItem, ...array.slice(index)];
}

// For Array
console.log( addArrayItemAtIndex(arr, 2,  159 ) );

// For Array of Objects
console.log( addArrayItemAtIndex(obj, 0, { name: "AMOOS"} ) );