best way to inject html using javascript

Keep your markup separate from your code:

You can embed the HTML snippets that you'll be using as hidden templates inside your HTML page and clone them on demand:

<style type="text/css">
#templates { display: none }
</style>
...
<script type="text/javascript">
var node = document.getElementById("tmp_audio").cloneNode(true);
node.id = ""; // Don't forget :)
// modify node contents with DOM manipulation
container.appendChild(node);
</script>
...
<div id="templates">
    <div id="tmp_audio">
        <a href="#" class="playButton">Play</a>
        <a href="#" class="muteUnmute">Mute</a>
        <div class="progressBarOuter"> 
            <div class="bytesLoaded"></div>
            <div class="progressBar"></div>
        </div>
        <div class="currentTime">0:00</div>
        <div class="totalTime">0:00</div>
    </div>
</div>

Update: Note that I've converted the id attributes in the template to class attributes. This is to avoid having multiple elements on your page with the same ids. You probably don't even need the classes. You can access elements with:

node.getElementsByTagName("div")[4].innerHTML =
    format(data.currentTime);

Alternatively, you can act on the HTML of the template:

<script type="text/javascript">
var tmp = document.getElementById("tmp_audio").innerHTML;
// modify template HTML with token replacement
container.innerHTML += tmp;
</script>

You can use

<script type="text/javascript">
    function appendHTML() {
        var wrapper = document.createElement("div");
        wrapper.innerHTML = '\
<a href="#" id="playButton">Play</a>\
<a href="javascript: void(0)" id="muteUnmute">Mute</a>\
<div id="progressBarOuter"> \
<div id="bytesLoaded"></div>\
    <div id="progressBar"></div>\
</div>\
<div id="currentTime">0:00</div>\
<div id="totalTime">0:00</div>\
';
        document.body.appendChild(wrapper);
    }
</script>

Shove the entire thing into a JS variable:

var html = '<a href="#" id="playButton">Play</a>';
html += '<a href="javascript: void(0)" id="muteUnmute">Mute</a>';
html += '<div id="progressBarOuter"><div id="bytesLoaded"></div><div id="progressBar"></div></div>';
html += '<div id="currentTime">0:00</div>';
html += '<div id="totalTime">0:00</div>';

Then:

document.getElementById("parentElement").innerHTML = html;

if you want theN:

document.getElementById("totalTime").innerHTML = "5:00";