String.prototype.charAt()

charAt(index)

var anyString = 'Brave new world';
console.log("The character at index 0   is '" + anyString.charAt()   + "'");
// No index was provided, used 0 as default

console.log("The character at index 0   is '" + anyString.charAt(0)   + "'");
console.log("The character at index 1   is '" + anyString.charAt(1)   + "'");
console.log("The character at index 2   is '" + anyString.charAt(2)   + "'");
console.log("The character at index 3   is '" + anyString.charAt(3)   + "'");
console.log("The character at index 4   is '" + anyString.charAt(4)   + "'");
console.log("The character at index 999 is '" + anyString.charAt(999) + "'");

The character at index 0   is 'B'

The character at index 0   is 'B'
The character at index 1   is 'r'
The character at index 2   is 'a'
The character at index 3   is 'v'
The character at index 4   is 'e'
The character at index 999 is ''

var str = 'A \uD87E\uDC04 Z'; // We could also use a non-BMP character directly
for (var i = 0, chr; i < str.length; i++) {
  if ((chr = getWholeChar(str, i)) === false) {
    continue;
  }
  // Adapt this line at the top of each loop, passing in the whole string and
  // the current iteration and returning a variable to represent the
  // individual character

  console.log(chr);
}

function getWholeChar(str, i) {
  var code = str.charCodeAt(i);

  if (Number.isNaN(code)) {
    return ''; // Position not found
  }
  if (code < 0xD800 || code > 0xDFFF) {
    return str.charAt(i);
  }

  // High surrogate (could change last hex to 0xDB7F to treat high private
  // surrogates as single characters)
  if (0xD800 <= code && code <= 0xDBFF) {
    if (str.length <= (i + 1)) {
      throw 'High surrogate without following low surrogate';
    }
    var next = str.charCodeAt(i + 1);
      if (0xDC00 > next || next > 0xDFFF) {
        throw 'High surrogate without following low surrogate';
      }
      return str.charAt(i) + str.charAt(i + 1);
  }
  // Low surrogate (0xDC00 <= code && code <= 0xDFFF)
  if (i === 0) {
    throw 'Low surrogate without preceding high surrogate';
  }
  var prev = str.charCodeAt(i - 1);

  // (could change last hex to 0xDB7F to treat high private
  // surrogates as single characters)
  if (0xD800 > prev || prev > 0xDBFF) {
    throw 'Low surrogate without preceding high surrogate';
  }
  // We can pass over low surrogates now as the second component
  // in a pair which we have already processed
  return false;
}

let str = 'A\uD87E\uDC04Z'  // We could also use a non-BMP character directly
for (let i = 0, chr; i < str.length; i++) {
  [chr, i] = getWholeCharAndI(str, i)

  // Adapt this line at the top of each loop, passing in the whole string and
  // the current iteration and returning an array with the individual character
  // and 'i' value (only changed if a surrogate pair)

  console.log(chr)
}

function getWholeCharAndI(str, i) {
  let code = str.charCodeAt(i)

  if (Number.isNaN(code)) {
    return ''  // Position not found
  }
  if (code < 0xD800 || code > 0xDFFF) {
    return [str.charAt(i), i]  // Normal character, keeping 'i' the same
  }

  // High surrogate (could change last hex to 0xDB7F to treat high private
  // surrogates as single characters)
  if (0xD800 <= code && code <= 0xDBFF) {
    if (str.length <= (i + 1)) {
      throw 'High surrogate without following low surrogate'
    }
    let next = str.charCodeAt(i + 1)
      if (0xDC00 > next || next > 0xDFFF) {
        throw 'High surrogate without following low surrogate'
      }
      return [str.charAt(i) + str.charAt(i + 1), i + 1]
  }

  // Low surrogate (0xDC00 <= code && code <= 0xDFFF)
  if (i === 0) {
    throw 'Low surrogate without preceding high surrogate'
  }

  let prev = str.charCodeAt(i - 1)

  // (could change last hex to 0xDB7F to treat high private surrogates
  // as single characters)
  if (0xD800 > prev || prev > 0xDBFF) {
    throw 'Low surrogate without preceding high surrogate'
  }

  // Return the next character instead (and increment)
  return [str.charAt(i + 1), i + 1]
}

function fixedCharAt(str, idx) {
  let ret = ''
  str += ''
  let end = str.length

  let surrogatePairs = /[\uD800-\uDBFF][\uDC00-\uDFFF]/g
  while ((surrogatePairs.exec(str)) != null) {
    let lastIdx = surrogatePairs.lastIndex
    if (lastIdx - 2 < idx) {
      idx++
    } else {
      break
    }
  }

  if (idx >= end || idx < 0) {
    return ''
  }

  ret += str.charAt(idx)

  if (/[\uD800-\uDBFF]/.test(ret) && /[\uDC00-\uDFFF]/.test(str.charAt(idx + 1))) {
    // Go one further, since one of the "characters" is part of a surrogate pair
    ret += str.charAt(idx + 1)
  }
  return ret
}