How to add a custom right-click menu to a webpage?

Answering your question - use contextmenu event, like below:

if (document.addEventListener) {
  document.addEventListener('contextmenu', function(e) {
    alert("You've tried to open context menu"); //here you draw your own menu
    e.preventDefault();
  }, false);
} else {
  document.attachEvent('oncontextmenu', function() {
    alert("You've tried to open context menu");
    window.event.returnValue = false;
  });
}
<body>
  Lorem ipsum...
</body>

But you should ask yourself, do you really want to overwrite default right-click behavior - it depends on application that you're developing.


JSFIDDLE


Was very useful for me. For the sake of people like me, expecting the drawing of menu, I put here the code I used to make the right-click menu:

$(document).ready(function() {


  if ($("#test").addEventListener) {
    $("#test").addEventListener('contextmenu', function(e) {
      alert("You've tried to open context menu"); //here you draw your own menu
      e.preventDefault();
    }, false);
  } else {

    //document.getElementById("test").attachEvent('oncontextmenu', function() {
    //$(".test").bind('contextmenu', function() {
    $('body').on('contextmenu', 'a.test', function() {


      //alert("contextmenu"+event);
      document.getElementById("rmenu").className = "show";
      document.getElementById("rmenu").style.top = mouseY(event) + 'px';
      document.getElementById("rmenu").style.left = mouseX(event) + 'px';

      window.event.returnValue = false;


    });
  }

});

// this is from another SO post...  
$(document).bind("click", function(event) {
  document.getElementById("rmenu").className = "hide";
});



function mouseX(evt) {
  if (evt.pageX) {
    return evt.pageX;
  } else if (evt.clientX) {
    return evt.clientX + (document.documentElement.scrollLeft ?
      document.documentElement.scrollLeft :
      document.body.scrollLeft);
  } else {
    return null;
  }
}

function mouseY(evt) {
  if (evt.pageY) {
    return evt.pageY;
  } else if (evt.clientY) {
    return evt.clientY + (document.documentElement.scrollTop ?
      document.documentElement.scrollTop :
      document.body.scrollTop);
  } else {
    return null;
  }
}
.show {
  z-index: 1000;
  position: absolute;
  background-color: #C0C0C0;
  border: 1px solid blue;
  padding: 2px;
  display: block;
  margin: 0;
  list-style-type: none;
  list-style: none;
}

.hide {
  display: none;
}

.show li {
  list-style: none;
}

.show a {
  border: 0 !important;
  text-decoration: none;
}

.show a:hover {
  text-decoration: underline !important;
}
<!-- jQuery should be at least version 1.7 -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/1.11.0/jquery.min.js"></script>
<script src="contextmenu.js"></script>
<link rel="stylesheet" href="contextmenu.css" />


<div id="test1">
  <a href="www.google.com" class="test">Google</a>
  <a href="www.google.com" class="test">Link 2</a>
  <a href="www.google.com" class="test">Link 3</a>
  <a href="www.google.com" class="test">Link 4</a>
</div>

<!-- initially hidden right-click menu -->
<div class="hide" id="rmenu">
  <ul>
    <li>
      <a href="http://www.google.com">Google</a>
    </li>

    <li>
      <a href="http://localhost:8080/login">Localhost</a>
    </li>

    <li>
      <a href="C:\">C</a>
    </li>
  </ul>
</div>