Cannot add click events to list items

delegate() is a deprecated jQuery method, and no such method exists in plain JS.
To attach an event handler in JS you'd use addEventListener, and for older versions of IE you'll need attachEvent as well, that's why it's a little tricky with cross browser event handlers.
onclick, onmouseenter etc. will work in all browsers, but it's consider a better practice to use addEventListener / attachEvent.

Also, you have to run the script after the elements are added to the DOM, otherwise they are not available. The usual way is to insert the script after the elements, or use a DOM ready event handler.

<html>
<head>
    <title>test</title>
</head>

<body>

<div id="topfriends">
  <h3>Top 4 Most Friendable Friends</h3>
  <ol id="top4list">
    <li>Brady</li>
    <li>Graham</li>
    <li>Josh</li>
    <li>Sean</li>
  </ol>
</div>

<script type="text/javascript">
    var lis = document.getElementById("top4list").getElementsByTagName('li');

    for (var i=0; i<lis.length; i++) {
        lis[i].addEventListener('click', doStuff, false);
    }

    function doStuff() {
        alert( this.innerHTML );
    }
</script>
</body>

FIDDLE


Let's do something like this

<ul id="parent-list">
    <li id="a">Item A</li>
    <li id="b">Item B</li>
    <li id="c">Item C</li>
    <li id="d">Item D</li>
    <li id="e">Item E</li>
    <li id="f">Item F</li>
</ul>

Now write the javascript for this

<script type="text/javascript">
    // locate your element and add the Click Event Listener
    document.getElementById("parent-list").addEventListener("click",function(e) {
        // e.target is our targetted element.
                    // try doing console.log(e.target.nodeName), it will result LI
        if(e.target && e.target.nodeName == "LI") {
            console.log(e.target.id + " was clicked");
        }
    });
</script>

Please refer to this write-up on Javascript Event Delegates http://davidwalsh.name/event-delegate

Also, below link is the fiddle that I created http://jsfiddle.net/REtHT/

hope this helps !