The library gives access to all APIs listed in the Google API Explorer and supports multiple browser environments and OAuth 2.0. To use the library, you will need to get have a developer key for the API that you wish to use. This can be obtained from the Google APIs console.
The Project home page for the library provides a Getting Started guide, Reference Documentation and Samples. The Getting started guide contains a straightforward example demonstrating the usage of the API. You simply need to load the library for the Google API that you plan to use, provide your key and make the client requests to the respective endpoints. A callback in your request will be invoked with the results of the request. The Google Apps Blog has a post where they have demonstrated how to use the library to access the Google Calendar API.