I pretty much just followed the directions here - http://scottjehl.github.io/picturefill/ In my markup I have something like:
<html>
<head>
<script src="scripts/vendor/picturefill.min.js"></script>
</head>
<body>
<picture>
<!--[if IE 9]><video style="display: none;"><![endif]-->
<source srcset="images/desktop-size.png" media="(min-width: 640px)">
<!--[if IE 9]></video><![endif]-->
<img class="app-layer-img" srcset="images/mobile-size.png">
</picture>
</body>
</html>
Note: IE9 is dumb which is why those silly IE conditionals are there =-[