The JavaScript client library does not support local pages and the file:// protocol. The application must be hosted on a server (can be localhost).
The JavaScript client library does not write any auth cookies. gapi.auth.getToken and gapi.auth.setToken provide access to the auth token.
Refresh the token by calling gapi.auth.authorize with the client ID, the scope and immediate:true as parameters.
Currently, the auth token expires after one hour. A common practice is to refresh the auth token after 45 minutes. If you refresh the auth token too often (every five minutes, for example) you will run into the refresh rate limit. (The rate limit is per-user, so the number of user connections is not an issue.)
The auth token's expires_in field will tell you the token's time to expiration.
The authSample.html file contains good examples of code that handles auth and token refreshes.
At this time, the JavaScript client library supports web applications only. For mobile devices you can use one of our other client libraries like the one for Objective-C
The JavaScript client library does not directly support logging the user out of the application. Typically, developers include a logout link to https://accounts.google.com/logout.
Since logging out of the application also logs the user out of the Google account, it is not recommended to log the user out unless the user requests this explicitly.
For a workaround that allows your application to log the user out programatically, see this topic in the JavaScript client library discussion group.