This is an example of how to use the Google Drive file picker and Google Drive API to retrieve files from Google Drive using pure JavaScript. At the time of writing (14th July 2013), Google have good examples for using these two APIs separately, but no documentation on using them together.
Note that this is just sample code, designed to be concise to demonstrate the API. In a production environment, you should include more error handling.
See a demo at http://stuff.dan.cx/js/filepicker/google/