What do I have to do to get the Modernizr module to work in Drupal?
Modernizer detects feature support in browsers and adds css classes to the HTML element based on those features.  You use those css classes to target newer features to browsers that support them.  While it will add HTML5 support to older browsers via the HTML5Shiv, it will not add CSS3 support.

To add support for CSS3 features in older browsers, you'll need to add a polyfill  Modernizer has a method called Modernizr.load() that lets you load the polyfill only when you need it.