Typically with storage service integration such as Dropbox or Google Drive, you can tap the sign out button in the lower right corner that looks like an open door.
There is a known issue with the Google Drive SDK (the code provided by Google that is added to OnSong to allow access to Google Drive) where the authentication information is not dropped immediately. The solution is to sign out of Google Drive and then close down OnSong. Reopening OnSong from scratch should then cause the Google Drive SDK to lose its authentication token, requiring a new authorization screen.
To close OnSong on modern versions of iOS, go to the home screen and then swipe up from the button edge of the device. This will display open apps. Flip through these apps and locate OnSong. You can then flick up on the tiny screen to close the app down. You can then return the home screen and open OnSong again.
Due to other issues in the Google Drive SDK, we have not been able to update to the latest version. We are watching to see if Google corrects flaws in the Google Drive SDK for iOS so that we can provide tighter and better integration with Google Drive.