To get a full list of the browser functionality that is tested check out the Modernizr docs. If the feature you need a test for isn't available it is fairly easy to add new tests as well.
You can try this example with an older version of Firefox and the text should indicate that there is no support for web sockets. Try again with a newer version of Google's Chrome browser and the page will indicate that there is support for web sockets.
The next example shows how to use the Modernizr CSS support. The key here is to know that the library will inject classes into the HTML tag. Those classes correspond to the functionality tests and are listed in the documentation. I am again testing for web sockets support and Modernizr will set the HTML class to either no-websockets or websockets and display one of two DIVs:
See this code in action: Modernizr CSS example.
For a much more detailed CSS example check out this A List Apart article.
If you need the information Modernizr assembles outside of the browser check out Modernizr on the server.