Use the Array.prototype.push method to append values to the end of an array:

// initialize array
var arr = [
  "Hi",
  "Hello",
  "Bonjour"
];

// append new value to the array
arr.push("Hola");

console.log(arr);

You can use the push() function to append more than one value to an array in a single call:

// initialize array
var arr = ["Hi", "Hello", "Bonjour", "Hola"];

// append multiple values to the array
arr.push("Salut", "Hey");

// display all values
for (var i = 0; i < arr.length; i++) {
  console.log(arr[i]);
}

Update

If you want to add the items of one array to another array, you can use firstArray.concat(secondArray):

var arr = [
  "apple",
  "banana",
  "cherry"
];

arr = arr.concat([
  "dragonfruit",
  "elderberry",
  "fig"
]);

console.log(arr);

Update

Just an addition to this answer if you want to prepend any value to the start of an array (i.e. first index) then you can use Array.prototype.unshift for this purpose.

var arr = [1, 2, 3];
arr.unshift(0);
console.log(arr);

It also supports appending multiple values at once just like push.