First, go to Main Menu, System, Preferences, Choose "Sound" choose the "Hardware" and "Output" tabs, see if the USB headphones (or similar) show up and are selected.
If so you will need to go to the preferences menu of the application you're trying to use and make sure the Audio Output is set to use the USB headphones instead of the default on board audio device.
Another possibility is that the device is muted, if so run "alsamixer" in a terminal and in the Alsamixer panel, press F6 to select the correct sound card (USB Speaker or similar) and make sure the volumes are not set too low and unmute them.
You might need to play around with these settings (as I had to also) to get them to work. Take note of what you change in case you need to change them back.