Google Hangouts have a clickable settings icon. You can use this in conjunction with Audacity and Pulse Audio Volume Control from the repository to check your camera, sound, and speakers.
To get to the settings go to http://hangouts.google.com, then click Video Call -> (click the x to not invite people) -> (Then click the) Gear icon
Check the video
From the Video dropdown select your video device. What you see is a verification of what will be broadcasted through Hangouts. If you see the video output you want, it checks... otherwise, of course. ensure your camera is properly connected and working. You might not see it if you have it currently connected to a different application.
Check the Microphone
From the Microphone dropdown select the audio device you will be using. You can test the input of the audio device by running the Pulse Audio Volume Control app. Click on the Input Devices tab. Then speak and notice the visual slider which will indicate the level. You can also use the Audacity app to record from the device so that you can hear how it sounds. Audacity has the same sound device listing that you will see in the Google Hangouts settings menu.
Since the apps you use to check the sound output, also locks the device to that app, you may have to exit out of the other sound apps to avoid conflict. This will also include Google Hangouts. The apps for checking the sound may not work when Google Hangouts is running. Also, Google Hangouts may also have a sound issue if the other apps for checking the sound is running. This will most likely be your system's default.
Check the speaker
From the speaker drop-down, select the speaker device you will be using. Click the speaker icon. What you hear is what you'll hear from your Google Hangouts session.
You can install Pulse Audio Volume Control and Audacity with these commands:
$ sudo apt install pavucontrol
$ sudo apt install audacity