When loading up a Live Room, you should first see a small pop up that contains drop downs for your mic and camera. However, you might see that it's empty like in the image below:

You can actually join to connect to the Live Room. However, you'll get another error related to permission flashing on the screen. You also won't be able to speak or be seen.

The most common cause is that your browser has set always deny or something similar in camera and mic permissions. To fix this in a Chrome browser, click the lock next to URL. This brings up a drop down. Make sure the browser allows the site access to camera and mic. Correct settings are shown here:

After that, reload the page. The next time you join the Live Room, the pop up will show up as normal.