What is a map method used for? It loops through an array of items and returns you a new array. The simplest example would be squaring the numbers in an array.

let nums = [1, 2, 3, 4];
let squares = nums.map((val) => val * val); // [1,4,9,16]

Now, how do I build a custom map function to do this same activity. Use Array.prototype.methodName to create a extension method for array.

Array.prototype.customMap = function () {
  // your implementation goes here
};

The above piece of code will create a customMap method associated with Array objects.

Now coming to the internal implementation of map function, it takes a callback function as input and returns the new array.

Array.prototype.customMap = function (callback) {
  let newArray = [];
  for (let i = 0; i < this.length; i++) {
    newArray.push(callback(this[i]));
  }
  return newArray;
};

In the above code snippet this refers to the current Array object passed to the map function.

The above implemenation is the basic version of map function, but the actual map method takes a callback function which has three things - currentValue, index and input array.

So on adding these parameters to the callback the code looks something as shown below.

Array.prototype.customMap = function (callback) {
  let newArray = [];
  for (let i = 0; i < this.length; i++) {
    newArray.push(callback(this[i], i, this));
  }
  return newArray;
};

The overall snippet with error checking added looks something as shown below

Array.prototype.customMap = function (callback) {
  // Validating if this is null
  if (this == null) {
    throw new TypeError("this is null");
  }

  // Validating if callback is a function
  if (typeof callback !== "function") {
    throw new TypeError(callback + " is not a function");
  }

  let newArray = [];
  for (let i = 0; i < this.length; i++) {
    newArray.push(callback(this[i], i, this));
  }
  return newArray;
};

This is a very basic version of map function. You could go through the complete polyfill code here at MDN.